Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 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×#20259354 | C2 | semidirect |
| 2. C2×#20259351 | C2 | semidirect |
| 4. C4⋊Q8×D191 | C2 | semidirect |
| 5. #27133058 | C2 | semidirect |
| 6. #27133057 | C2 | semidirect |
| 7. #27133055 | C2 | semidirect |
| 8. #27133041 | C2 | semidirect |
| 9. #27133034 | C2 | semidirect |
| 10. #27132615 | C2 | semidirect |
| 11. #497×C191 | C2 | semidirect |
| 63. #15690270 | D4 | semidirect |
| 124. Dic191 | #137 | semidirect |
| 130. C191 | #3152 | semidirect |
| 139. #497 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259354 | 2 |
| C2×#20259351 | 2 |
| #27133212 | 2 |
| C4⋊Q8×D191 | 2 |
| #27133058 | 2 |
| #27133057 | 2 |
| #27133055 | 2 |
| #27133041 | 2 |
| #27133034 | 2 |
| #27132615 | 2 |
| #497×C191 | 2 |
| #3152 | 191 |