Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133220 | C2 | semidirect |
| 2. #27132967 | C2 | semidirect |
| 3. #27132958 | C2 | semidirect |
| 4. #27132953 | C2 | semidirect |
| 5. #27132919 | C2 | semidirect |
| 7. #27132882 | C2 | semidirect |
| 8. #27132873 | C2 | semidirect |
| 9. #27132868 | C2 | semidirect |
| 10. #27132687 | C2 | semidirect |
| 133. C191 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27132967 | 2 |
| #27132958 | 2 |
| #27132953 | 2 |
| #27132919 | 2 |
| #27132907 | 2 |
| #27132882 | 2 |
| #27132873 | 2 |
| #27132868 | 2 |
| #27132687 | 2 |
| #529×C191 | 2 |
| #3252 | 191 |