Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259348 | C2 | semidirect |
| 3. C2×#20259342 | C2 | semidirect |
| 4. C22×#15690275 | C2 | semidirect |
| 5. #27133239 | C2 | semidirect |
| 6. #27133058 | C2 | semidirect |
| 7. #27133050 | C2 | semidirect |
| 8. #27133045 | C2 | semidirect |
| 9. #27133035 | C2 | semidirect |
| 10. #27132619 | C2 | semidirect |
| 11. #535×C191 | C2 | semidirect |
| 17. C2×#15690277 | C22 | semidirect |
| 18. C2×#15690277 | C22 | semidirect |
| 23. C2×#15690275 | C22 | semidirect |
| 24. C2×#15690275 | C22 | semidirect |
| 25. C2×#15690274 | C22 | semidirect |
| 27. C2×#15690272 | C22 | semidirect |
| 30. #20259322 | C22 | semidirect |
| 31. #20259310 | C22 | semidirect |
| 34. #20259233 | C22 | semidirect |
| 35. C4×C191⋊C8 | C22 | semidirect |
| 64. #15690271 | D4 | semidirect |
| 65. C2×C191⋊C8 | D4 | semidirect |
| 148. C191 | #3154 | semidirect |
| 155. #535 | 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×#20259348 | 2 |
| C2×#20259342 | 2 |
| C22×#15690275 | 2 |
| #27133239 | 2 |
| #27133058 | 2 |
| #27133050 | 2 |
| #27133045 | 2 |
| #27133035 | 2 |
| #27132619 | 2 |
| #535×C191 | 2 |
| #3154 | 191 |