Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
| prime radical | C23×C22⋊D271 | C2 |
| hypercenter | #379 | D271 |
| hypocenter | C271 | #2405 |
| LCS | G ▷ C23×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#22576144 | C2 | semidirect |
| 3. C22×C22⋊Dic271 | C2 | semidirect |
| 4. #31773813 | C2 | semidirect |
| 5. #31773774 | C2 | semidirect |
| 6. #31773772 | C2 | semidirect |
| 7. #31773752 | C2 | semidirect |
| 8. #379×C271 | C2 | semidirect |
| 15. C23×Dic271 | C22 | semidirect |
| 16. C23×Dic271 | C22 | semidirect |
| 18. C2×C4⋊Dic271 | C22 | semidirect |
| 21. C2×C22⋊Dic271 | C22 | semidirect |
| 22. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 23. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 24. C271⋊#95 | C22 | semidirect |
| 27. C2×C22⋊C4×C271 | C22 | semidirect |
| 28. C2×C22⋊C4×C271 | C22 | semidirect |
| 119. C22×C271 | #123 | semidirect |
| 142. C271 | #2405 | semidirect |
| 151. #379 | D271 | semidirect |
| 169. C2×C22⋊C4 | C2×D271 | semidirect |
| 170. C2×C22⋊C4 | C2×D271 | semidirect |
| 268. C22 | #22576144 | 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×#22576144 | 2 |
| C22×C22⋊Dic271 | 2 |
| #31773813 | 2 |
| #31773774 | 2 |
| #31773772 | 2 |
| #31773752 | 2 |
| #379×C271 | 2 |
| #2405 | 271 |