Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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×#380 | C2 |
| hypercenter | #380 | D19 |
| hypocenter | C19 | #2847 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D19 | C2 | semidirect |
| 2. C2×#10597341 | C2 | semidirect |
| 3. C2×#10597376 | C2 | semidirect |
| 4. C2×#10597328 | C2 | semidirect |
| 5. #11926422 | C2 | semidirect |
| 6. #11926421 | C2 | semidirect |
| 7. #11926401 | C2 | semidirect |
| 8. C19×#380 | C2 | semidirect |
| 14. C22×D76 | C22 | semidirect |
| 19. C2×C4⋊C4×C19 | C22 | semidirect |
| 23. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 25. C2×C4⋊Dic19 | C22 | semidirect |
| 28. C19×#95 | C22 | semidirect |
| 29. C19⋊#95 | C22 | semidirect |
| 35. C23×D19 | D4 | semidirect |
| 39. C22×C4×C19 | D4 | semidirect |
| 61. C2×C4×D19 | D4 | semidirect |
| 116. C22×C19 | #121 | semidirect |
| 134. C2×D19 | #121 | semidirect |
| 137. C4×C19 | #120 | semidirect |
| 147. #380 | D19 | semidirect |
| 170. C2×C4⋊C4 | C2×D19 | semidirect |
| 176. #95 | C2×D19 | semidirect |
| 177. C19 | #2847 | semidirect |
| 206. C22×C4 | D76 | semidirect |
| 276. C22 | #10597341 | semidirect |
| 286. C4 | #10597328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D19 | 2 |
| C2×#10597341 | 2 |
| C2×#10597376 | 2 |
| C2×#10597328 | 2 |
| #11926422 | 2 |
| #11926421 | 2 |
| #11926401 | 2 |
| C19×#380 | 2 |
| #2847 | 19 |