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×#20259355 | C2 | semidirect |
| 2. C2×#20259342 | C2 | semidirect |
| 3. C22×#15690275 | C2 | semidirect |
| 4. #27133234 | C2 | semidirect |
| 5. #27133230 | C2 | semidirect |
| 6. #27133054 | C2 | semidirect |
| 7. #27133051 | C2 | semidirect |
| 8. #27133046 | C2 | semidirect |
| 9. #27133034 | C2 | semidirect |
| 10. #27132621 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C191 | C2 | semidirect |
| 16. C2×Dic764 | C22 | semidirect |
| 17. C2×#15690277 | C22 | semidirect |
| 18. C2×#15690276 | C22 | semidirect |
| 22. C2×#15690275 | C22 | semidirect |
| 23. C2×#15690274 | C22 | semidirect |
| 24. C2×#15690272 | C22 | semidirect |
| 26. #20259320 | C22 | semidirect |
| 29. #20259309 | C22 | semidirect |
| 35. #20259232 | C22 | semidirect |
| 36. C8×Dic191 | C22 | semidirect |
| 63. C2×C191⋊C8 | D4 | semidirect |
| 86. M16×C191 | D4 | semidirect |
| 148. C191 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D191 | semidirect |
| 226. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259342 | 2 |
| C22×#15690275 | 2 |
| #27133234 | 2 |
| #27133230 | 2 |
| #27133054 | 2 |
| #27133051 | 2 |
| #27133046 | 2 |
| #27133034 | 2 |
| #27132621 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3154 | 191 |