Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
952 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×#41×C19 | C2 |
| hypercenter | C22×#41 | D19 |
| hypocenter | C19 | #2431 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597386 | C2 | semidirect |
| 2. C2×#10597393 | C2 | semidirect |
| 3. C2×#10597376 | C2 | semidirect |
| 4. #11926452 | C2 | semidirect |
| 5. #11926451 | C2 | semidirect |
| 6. #11926447 | C2 | semidirect |
| 7. #11926423 | C2 | semidirect |
| 8. C4×C22⋊Dic19 | C2 | semidirect |
| 9. C22×#41×C19 | C2 | semidirect |
| 39. C2×Q8×C19 | D4 | semidirect |
| 45. C2×D4×C19 | D4 | semidirect |
| 51. C22×C4×C19 | D4 | semidirect |
| 112. C2×Dic19 | #41 | semidirect |
| 141. C22×#41 | D19 | semidirect |
| 181. C19 | #2431 | semidirect |
| 188. C2×Q8 | C22⋊D19 | semidirect |
| 202. C2×D4 | C22⋊D19 | semidirect |
| 211. C22×C4 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597386 | 2 |
| C2×#10597393 | 2 |
| C2×#10597376 | 2 |
| #11926452 | 2 |
| #11926451 | 2 |
| #11926447 | 2 |
| #11926423 | 2 |
| C4×C22⋊Dic19 | 2 |
| C22×#41×C19 | 2 |
| #2431 | 19 |