Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
732 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C2×C4×D4×C19 | C2 |
| hypercenter | C2×C4×D4 | D19 |
| hypocenter | C19 | #2535 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597384 | C2 | semidirect |
| 2. C2×C4×D76 | C2 | semidirect |
| 3. #11926469 | C2 | semidirect |
| 4. #11926453 | C2 | semidirect |
| 5. #11926423 | C2 | semidirect |
| 6. #11926410 | C2 | semidirect |
| 7. #11926401 | C2 | semidirect |
| 8. C2×C4×D4×C19 | C2 | semidirect |
| 32. C2×D4×C19 | D4 | semidirect |
| 51. C42×C19 | D4 | semidirect |
| 116. C2×C4×D4 | D19 | semidirect |
| 148. C19 | #2535 | semidirect |
| 158. C2×D4 | D76 | semidirect |
| 177. C42 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597384 | 2 |
| C2×C4×D76 | 2 |
| #11926469 | 2 |
| #11926453 | 2 |
| #11926423 | 2 |
| #11926410 | 2 |
| #11926401 | 2 |
| C2×C4×D4×C19 | 2 |
| #2535 | 19 |