Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#20259369 | C2 | semidirect |
| 2. C22×#15690275 | C2 | semidirect |
| 3. #27133230 | C2 | semidirect |
| 4. #27132805 | C2 | semidirect |
| 5. #27132800 | C2 | semidirect |
| 6. #27132673 | C2 | semidirect |
| 7. #27132659 | C2 | semidirect |
| 8. #27132631 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C191 | C2 | semidirect |
| 15. C2×#15690286 | C22 | semidirect |
| 18. C2×Q8×D191 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259246 | C22 | semidirect |
| 29. #20259243 | C22 | semidirect |
| 30. (C2×D191)⋊C8 | C22 | semidirect |
| 48. C2×Dic382 | D4 | semidirect |
| 69. #41×C191 | D4 | semidirect |
| 145. C191 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D191 | semidirect |
| 191. #41 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259369 | 2 |
| C22×#15690275 | 2 |
| #27133230 | 2 |
| #27132805 | 2 |
| #27132800 | 2 |
| #27132673 | 2 |
| #27132659 | 2 |
| #27132631 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3010 | 191 |