Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C23×Q8×C19 | C2 |
| prime radical | C22×C22⋊D19 | C22 |
| hypercenter | C23×Q8 | D19 |
| hypocenter | C19 | #2409 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597392 | C2 | semidirect |
| 3. #11926463 | C2 | semidirect |
| 4. #11926455 | C2 | semidirect |
| 5. #11926451 | C2 | semidirect |
| 7. #11926417 | C2 | semidirect |
| 8. #11926404 | C2 | semidirect |
| 9. C23×Q8×C19 | C2 | semidirect |
| 38. C2×Q8×C19 | D4 | semidirect |
| 48. C2×C22⋊D19 | Q8 | semidirect |
| 73. C22×D19 | C2×Q8 | semidirect |
| 95. C2×Dic19 | C2×Q8 | semidirect |
| 102. C22×C19 | C22⋊Q8 | semidirect |
| 120. C23×Q8 | D19 | semidirect |
| 157. C19 | #2409 | semidirect |
| 165. C2×Q8 | C22⋊D19 | semidirect |
| 233. C22 | #10597392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597392 | 2 |
| C2×C4×C22⋊D19 | 2 |
| #11926463 | 2 |
| #11926455 | 2 |
| #11926451 | 2 |
| #11926423 | 2 |
| #11926417 | 2 |
| #11926404 | 2 |
| C23×Q8×C19 | 2 |
| #2409 | 19 |