Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 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 | #123×C263 | C2 |
| hypercenter | #123 | D263 |
| hypocenter | C263 | #553 |
| LCS | G ▷ C22×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22554465 | C2 | semidirect |
| 2. #22554463 | C2 | semidirect |
| 3. #22554460 | C2 | semidirect |
| 4. #22554452 | C2 | semidirect |
| 5. #22554443 | C2 | semidirect |
| 6. #22554443 | C2 | semidirect |
| 7. #22554442 | C2 | semidirect |
| 8. #22554441 | C2 | semidirect |
| 9. #22554432 | C2 | semidirect |
| 10. C4×C22⋊D263 | C2 | semidirect |
| 11. C4×C22⋊D263 | C2 | semidirect |
| 12. (C22⋊D263)⋊C4 | C2 | semidirect |
| 13. #22554426 | C2 | semidirect |
| 14. C4⋊C4×D263 | C2 | semidirect |
| 15. #123×C263 | C2 | semidirect |
| 109. C263 | #553 | semidirect |
| 115. #123 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554465 | 2 |
| #22554463 | 2 |
| #22554460 | 2 |
| #22554452 | 2 |
| #22554443 | 2 |
| #22554442 | 2 |
| #22554441 | 2 |
| #22554432 | 2 |
| C4×C22⋊D263 | 2 |
| (C22⋊D263)⋊C4 | 2 |
| #22554426 | 2 |
| C4⋊C4×D263 | 2 |
| #123×C263 | 2 |
| #553 | 263 |