Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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×#20259342 | C2 | semidirect |
| 2. C2×#20259329 | C2 | semidirect |
| 3. #27133241 | C2 | semidirect |
| 4. #27132919 | C2 | semidirect |
| 5. #27132914 | C2 | semidirect |
| 6. #27132894 | C2 | semidirect |
| 7. #27132890 | C2 | semidirect |
| 8. C2×#20259253 | C2 | semidirect |
| 9. #27132664 | C2 | semidirect |
| 10. #27132662 | C2 | semidirect |
| 11. #537×C191 | C2 | semidirect |
| 58. C2×C191⋊C8 | D4 | semidirect |
| 152. C191 | #3060 | semidirect |
| 157. #537 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259342 | 2 |
| C2×#20259329 | 2 |
| #27133241 | 2 |
| #27132919 | 2 |
| #27132914 | 2 |
| #27132894 | 2 |
| #27132890 | 2 |
| C2×#20259253 | 2 |
| #27132664 | 2 |
| #27132662 | 2 |
| #537×C191 | 2 |
| #3060 | 191 |