Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1564 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D271 |
| commutator, socle, cosocle | C23×C271 | C24 |
| Fitting | C23×D4×C271 | C2 |
| hypercenter | C23×D4 | D271 |
| hypocenter | C271 | #2403 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D271 | C2 | semidirect |
| 2. C2×#22576129 | C2 | semidirect |
| 3. C2×#22576128 | C2 | semidirect |
| 4. #31773805 | C2 | semidirect |
| 5. #31773777 | C2 | semidirect |
| 6. #31773776 | C2 | semidirect |
| 7. #31773753 | C2 | semidirect |
| 8. C23×D4×C271 | C2 | semidirect |
| 9. C24×D271 | C22 | semidirect |
| 13. C22×C22⋊D271 | C22 | semidirect |
| 14. C22×C22⋊D271 | C22 | semidirect |
| 15. C23×Dic271 | C22 | semidirect |
| 18. C2×C22⋊Dic271 | C22 | semidirect |
| 19. C2×C22⋊Dic271 | C22 | semidirect |
| 20. C2×C22⋊Dic271 | C22 | semidirect |
| 21. C2×C22⋊Dic271 | C22 | semidirect |
| 22. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 23. C271⋊#95 | C22 | semidirect |
| 25. C25×C271 | C22 | semidirect |
| 29. C22×D4×C271 | C22 | semidirect |
| 30. C23×C4×C271 | C22 | semidirect |
| 45. C2×C22⋊D271 | D4 | semidirect |
| 62. C24×C271 | D4 | semidirect |
| 73. C2×D4×C271 | D4 | semidirect |
| 85. C22×D271 | C2×D4 | semidirect |
| 95. C2×Dic271 | C2×D4 | semidirect |
| 120. C23×C271 | C2×D4 | semidirect |
| 127. C2×C4×C271 | C2×D4 | semidirect |
| 145. C22×C271 | #120 | semidirect |
| 146. C22×C271 | #120 | semidirect |
| 169. C271 | #2403 | semidirect |
| 172. C23×D4 | D271 | semidirect |
| 181. C25 | C2×D271 | semidirect |
| 190. C22×D4 | C2×D271 | semidirect |
| 192. C23×C4 | C2×D271 | semidirect |
| 213. C24 | C22⋊D271 | semidirect |
| 234. C2×D4 | C22⋊D271 | semidirect |
| 280. C23 | C2×C22⋊D271 | semidirect |
| 297. C2×C4 | C2×C22⋊D271 | semidirect |
| 321. C22 | #22576128 | semidirect |
| 322. C22 | #22576129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D271 | 2 |
| C2×#22576129 | 2 |
| C2×#22576128 | 2 |
| #31773805 | 2 |
| #31773777 | 2 |
| #31773776 | 2 |
| #31773753 | 2 |
| C23×D4×C271 | 2 |
| #2403 | 271 |