Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 125 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×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#397 | C2 |
| hypercenter | #397 | D19 |
| hypocenter | C19 | #2815 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597341 | C2 | semidirect |
| 2. C2×#10597330 | C2 | semidirect |
| 3. #11926473 | C2 | semidirect |
| 4. #11926470 | C2 | semidirect |
| 5. #11926454 | C2 | semidirect |
| 6. #11926454 | C2 | semidirect |
| 7. #11926453 | C2 | semidirect |
| 8. #11926453 | C2 | semidirect |
| 9. #11926453 | C2 | semidirect |
| 10. #11926406 | C2 | semidirect |
| 11. C19×#397 | C2 | semidirect |
| 66. C2×C4×D19 | D4 | semidirect |
| 164. #397 | D19 | semidirect |
| 205. C19 | #2815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597341 | 2 |
| C2×#10597330 | 2 |
| #11926473 | 2 |
| #11926470 | 2 |
| #11926454 | 2 |
| #11926453 | 2 |
| #11926406 | 2 |
| C19×#397 | 2 |
| #2815 | 19 |