Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic382 | C2 | semidirect |
| 2. #27132996 | C2 | semidirect |
| 4. #27132967 | C2 | semidirect |
| 5. #27132882 | C2 | semidirect |
| 6. #27132818 | C2 | semidirect |
| 8. #27132768 | C2 | semidirect |
| 9. #27132763 | C2 | semidirect |
| 10. #27132720 | C2 | semidirect |
| 131. C191 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic382 | 2 |
| #27132996 | 2 |
| #27132979 | 2 |
| #27132967 | 2 |
| #27132882 | 2 |
| #27132818 | 2 |
| #27132801 | 2 |
| #27132768 | 2 |
| #27132763 | 2 |
| #27132720 | 2 |
| #529×C191 | 2 |
| #3117 | 191 |