Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
| prime radical | C2×#16862375 | C2 |
| hypercenter | #123 | D263 |
| hypocenter | C263 | #536 |
| LCS | G ▷ C22×C263 ▷ C263 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic526 | C2 | semidirect |
| 3. #22554469 | C2 | semidirect |
| 4. #22554456 | C2 | semidirect |
| 5. #22554454 | C2 | semidirect |
| 6. #22554453 | C2 | semidirect |
| 7. #22554451 | C2 | semidirect |
| 8. #22554448 | C2 | semidirect |
| 9. #22554447 | C2 | semidirect |
| 10. #22554426 | C2 | semidirect |
| 11. #123×C263 | C2 | semidirect |
| 79. C263 | #536 | semidirect |
| 88. #123 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862375 | 2 |
| C22×Dic526 | 2 |
| #22554469 | 2 |
| #22554456 | 2 |
| #22554454 | 2 |
| #22554453 | 2 |
| #22554451 | 2 |
| #22554448 | 2 |
| #22554447 | 2 |
| #22554426 | 2 |
| #123×C263 | 2 |
| #536 | 263 |