Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20259296 | C2 | semidirect |
| 2. #27132981 | C2 | semidirect |
| 3. #27132979 | C2 | semidirect |
| 4. #27132914 | C2 | semidirect |
| 5. #27132797 | C2 | semidirect |
| 6. #27132796 | C2 | semidirect |
| 7. #27132627 | C2 | semidirect |
| 8. C2×#121×C191 | C2 | semidirect |
| 9. C22×D764 | C22 | semidirect |
| 11. C2×#15690272 | C22 | semidirect |
| 12. C2×#15690271 | C22 | semidirect |
| 16. #20259296 | C22 | semidirect |
| 17. C2×C4⋊Dic191 | C22 | semidirect |
| 19. #20259253 | C22 | semidirect |
| 20. #20259243 | C22 | semidirect |
| 21. #20259242 | C22 | semidirect |
| 22. C22⋊(C191⋊C8) | C22 | semidirect |
| 23. C22⋊(C191⋊C8) | C22 | semidirect |
| 25. C22×D4×C191 | C22 | semidirect |
| 30. #121×C191 | C22 | semidirect |
| 31. C2×C4⋊C4×C191 | C22 | semidirect |
| 138. C191 | #3192 | semidirect |
| 141. C2×#121 | D191 | semidirect |
| 151. C22×D4 | C2×D191 | semidirect |
| 162. #121 | C2×D191 | semidirect |
| 164. C2×C4⋊C4 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259296 | 2 |
| #27132981 | 2 |
| #27132979 | 2 |
| #27132914 | 2 |
| #27132797 | 2 |
| #27132796 | 2 |
| #27132627 | 2 |
| C2×#121×C191 | 2 |
| #3192 | 191 |