Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×C19×#117 | C2 |
| hypercenter | C2×#117 | D19 |
| hypocenter | C19 | #2619 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597320 | C2 | semidirect |
| 2. C2×#10597376 | C2 | semidirect |
| 3. #11926461 | C2 | semidirect |
| 4. #11926453 | C2 | semidirect |
| 5. #11926446 | C2 | semidirect |
| 6. #11926410 | C2 | semidirect |
| 7. C2×C19×#117 | C2 | semidirect |
| 27. C22×C4×C19 | D4 | semidirect |
| 43. C42×C19 | D4 | semidirect |
| 94. C2×#117 | D19 | semidirect |
| 120. C19 | #2619 | semidirect |
| 133. C22×C4 | D76 | semidirect |
| 144. C42 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597320 | 2 |
| C2×#10597376 | 2 |
| #11926461 | 2 |
| #11926453 | 2 |
| #11926446 | 2 |
| #11926410 | 2 |
| C2×C19×#117 | 2 |
| #2619 | 19 |