Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D263 |
| commutator, socle, cosocle | C22×C263 | C24 |
| Fitting | #121×C263 | C2 |
| hypercenter | #121 | D263 |
| hypocenter | C263 | #540 |
| LCS | G ▷ C22×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22554466 | C2 | semidirect |
| 2. #22554461 | C2 | semidirect |
| 3. #22554454 | C2 | semidirect |
| 4. #22554452 | C2 | semidirect |
| 5. #22554444 | C2 | semidirect |
| 6. #22554442 | C2 | semidirect |
| 7. #22554441 | C2 | semidirect |
| 8. D4×Dic263 | C2 | semidirect |
| 9. #22554432 | C2 | semidirect |
| 10. #22554429 | C2 | semidirect |
| 11. #121×C263 | C2 | semidirect |
| 79. C263 | #540 | semidirect |
| 88. #121 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554466 | 2 |
| #22554461 | 2 |
| #22554454 | 2 |
| #22554452 | 2 |
| #22554444 | 2 |
| #22554442 | 2 |
| #22554441 | 2 |
| D4×Dic263 | 2 |
| #22554432 | 2 |
| #22554429 | 2 |
| #121×C263 | 2 |
| #540 | 263 |