Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C4×C22⋊C4×C19 | C2 |
| hypercenter | C4×C22⋊C4 | D19 |
| hypocenter | C19 | #2433 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D76 | C2 | semidirect |
| 2. C2×#10597320 | C2 | semidirect |
| 3. C2×#10597376 | C2 | semidirect |
| 4. C2×#10597328 | C2 | semidirect |
| 5. #11926454 | C2 | semidirect |
| 6. #11926446 | C2 | semidirect |
| 7. C4×C22⋊C4×C19 | C2 | semidirect |
| 15. C22×D76 | C22 | semidirect |
| 16. C22×D76 | C22 | semidirect |
| 18. C2×C42×C19 | C22 | semidirect |
| 20. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 22. C2×C4⋊Dic19 | C22 | semidirect |
| 25. C19×#95 | C22 | semidirect |
| 34. C22×C4×C19 | D4 | semidirect |
| 51. C2×D76 | D4 | semidirect |
| 52. C22⋊C4×C19 | D4 | semidirect |
| 82. C2×C4×C19 | C2×D4 | semidirect |
| 94. C22×C19 | #127 | semidirect |
| 111. C4×C19 | #120 | semidirect |
| 119. C4×C22⋊C4 | D19 | semidirect |
| 143. C2×C42 | C2×D19 | semidirect |
| 144. #95 | C2×D19 | semidirect |
| 145. C19 | #2433 | semidirect |
| 168. C22×C4 | D76 | semidirect |
| 175. C22⋊C4 | D76 | semidirect |
| 208. C2×C4 | C2×D76 | semidirect |
| 223. C22 | #10597320 | semidirect |
| 231. C4 | #10597328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D76 | 2 |
| C2×#10597320 | 2 |
| C2×#10597376 | 2 |
| C2×#10597328 | 2 |
| #11926454 | 2 |
| #11926446 | 2 |
| C4×C22⋊C4×C19 | 2 |
| #2433 | 19 |