Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597370 | C2 | semidirect |
| 2. #11926474 | C2 | semidirect |
| 3. #11926472 | C2 | semidirect |
| 4. #11926469 | C2 | semidirect |
| 5. #11926464 | C2 | semidirect |
| 7. #11926456 | C2 | semidirect |
| 8. #11926428 | C2 | semidirect |
| 9. #11926417 | C2 | semidirect |
| 10. #11926407 | C2 | semidirect |
| 175. C19 | #2638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597370 | 2 |
| #11926474 | 2 |
| #11926472 | 2 |
| #11926469 | 2 |
| #11926464 | 2 |
| #11926458 | 2 |
| #11926456 | 2 |
| #11926428 | 2 |
| #11926417 | 2 |
| #11926407 | 2 |
| C2×C4×D4×C19 | 2 |
| #2638 | 19 |