Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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×#390 | C2 |
| hypercenter | #390 | D19 |
| hypocenter | C19 | #2555 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597331 | C2 | semidirect |
| 2. C2×#10597330 | C2 | semidirect |
| 3. #11926464 | C2 | semidirect |
| 4. #11926461 | C2 | semidirect |
| 5. #11926452 | C2 | semidirect |
| 6. #11926432 | C2 | semidirect |
| 7. #11926420 | C2 | semidirect |
| 8. C4×(C2×D19)⋊C4 | C2 | semidirect |
| 9. C19×#390 | C2 | semidirect |
| 66. (C2×D19)⋊C4 | D4 | semidirect |
| 141. #390 | D19 | semidirect |
| 175. C19 | #2555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597331 | 2 |
| C2×#10597330 | 2 |
| #11926464 | 2 |
| #11926461 | 2 |
| #11926452 | 2 |
| #11926432 | 2 |
| #11926420 | 2 |
| C4×(C2×D19)⋊C4 | 2 |
| C19×#390 | 2 |
| #2555 | 19 |