Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20259352 | C2 | semidirect |
| 2. C2×#20259328 | C2 | semidirect |
| 4. #27133239 | C2 | semidirect |
| 5. #27132920 | C2 | semidirect |
| 6. #27132908 | C2 | semidirect |
| 7. #27132903 | C2 | semidirect |
| 8. #27132891 | C2 | semidirect |
| 9. #27132706 | C2 | semidirect |
| 10. C2×#20259247 | C2 | semidirect |
| 11. #416×C191 | C2 | semidirect |
| 58. #15690271 | D4 | semidirect |
| 143. C191 | #3063 | semidirect |
| 154. #416 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C2×#20259328 | 2 |
| #27133241 | 2 |
| #27133239 | 2 |
| #27132920 | 2 |
| #27132908 | 2 |
| #27132903 | 2 |
| #27132891 | 2 |
| #27132706 | 2 |
| C2×#20259247 | 2 |
| #416×C191 | 2 |
| #3063 | 191 |