Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #27133291 | C2 | semidirect |
| 3. #27133028 | C2 | semidirect |
| 4. #27133023 | C2 | semidirect |
| 5. #27133018 | C2 | semidirect |
| 6. #27133010 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132665 | C2 | semidirect |
| 9. #27132660 | C2 | semidirect |
| 10. C2×#20259244 | C2 | semidirect |
| 11. #405×C191 | C2 | semidirect |
| 14. #20259322 | C22 | semidirect |
| 17. #20259314 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259247 | C22 | semidirect |
| 33. #20259244 | C22 | semidirect |
| 34. #20259244 | C22 | semidirect |
| 35. #20259244 | C22 | semidirect |
| 39. #97×C191 | C22 | semidirect |
| 40. C4×C8×C191 | C22 | semidirect |
| 135. C191 | #3136 | semidirect |
| 147. #405 | D191 | semidirect |
| 175. #97 | C2×D191 | semidirect |
| 176. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133232 | 2 |
| #27133028 | 2 |
| #27133023 | 2 |
| #27133018 | 2 |
| #27133010 | 2 |
| #27132669 | 2 |
| #27132665 | 2 |
| #27132660 | 2 |
| C2×#20259244 | 2 |
| #405×C191 | 2 |
| #3136 | 191 |