Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1564 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #379×C271 | C2 |
| hypercenter | #379 | D271 |
| hypocenter | C271 | #2403 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D271 | C2 | semidirect |
| 2. C2×#22576130 | C2 | semidirect |
| 3. #31773806 | C2 | semidirect |
| 4. #31773774 | C2 | semidirect |
| 5. #379×C271 | C2 | semidirect |
| 6. C24×D271 | C22 | semidirect |
| 7. C22×D1084 | C22 | semidirect |
| 11. C22×C22⋊D271 | C22 | semidirect |
| 12. C23×Dic271 | C22 | semidirect |
| 14. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 15. C271⋊#95 | C22 | semidirect |
| 17. C2×C22⋊C4×C271 | C22 | semidirect |
| 18. C2×C22⋊C4×C271 | C22 | semidirect |
| 32. C2×C22⋊D271 | D4 | semidirect |
| 39. C24×C271 | D4 | semidirect |
| 53. C22×D271 | C2×D4 | semidirect |
| 60. C2×Dic271 | C2×D4 | semidirect |
| 81. C22×C271 | #120 | semidirect |
| 99. C271 | #2403 | semidirect |
| 105. #379 | D271 | semidirect |
| 116. C2×C22⋊C4 | C2×D271 | semidirect |
| 117. C2×C22⋊C4 | C2×D271 | semidirect |
| 126. C24 | D1084 | semidirect |
| 187. C22 | #22576130 | 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×#22576130 | 2 |
| #31773806 | 2 |
| #31773774 | 2 |
| #379×C271 | 2 |
| #2403 | 271 |