Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20259281 | C2 | semidirect |
| 2. #27132984 | C2 | semidirect |
| 3. #27132979 | C2 | semidirect |
| 4. #27132974 | C2 | semidirect |
| 5. #27132703 | C2 | semidirect |
| 6. #27132668 | C2 | semidirect |
| 7. #27132627 | C2 | semidirect |
| 13. #20259281 | C22 | semidirect |
| 14. C2×C4⋊Dic191 | C22 | semidirect |
| 15. C2×C4⋊Dic191 | C22 | semidirect |
| 18. #20259255 | C22 | semidirect |
| 19. #20259253 | C22 | semidirect |
| 20. #20259243 | C22 | semidirect |
| 21. #20259243 | C22 | semidirect |
| 22. C22⋊(C191⋊C8) | C22 | semidirect |
| 23. C22⋊(C191⋊C8) | C22 | semidirect |
| 125. C191 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259281 | 2 |
| #27132984 | 2 |
| #27132979 | 2 |
| #27132974 | 2 |
| #27132703 | 2 |
| #27132668 | 2 |
| #27132627 | 2 |
| C2×#121×C191 | 2 |
| #3094 | 191 |