Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133146 | C2 | semidirect |
| 2. #27132984 | C2 | semidirect |
| 3. #27132984 | C2 | semidirect |
| 4. #27132979 | C2 | semidirect |
| 5. #27132974 | C2 | semidirect |
| 6. #27132706 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132668 | C2 | semidirect |
| 9. C2×#20259243 | C2 | semidirect |
| 10. #27132630 | C2 | semidirect |
| 18. #20259281 | C22 | semidirect |
| 20. C2×C4⋊Dic191 | C22 | semidirect |
| 21. #20259255 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259253 | C22 | semidirect |
| 31. C22⋊(C191⋊C8) | C22 | semidirect |
| 32. C22⋊(C191⋊C8) | C22 | semidirect |
| 134. C191 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133146 | 2 |
| #27132984 | 2 |
| #27132979 | 2 |
| #27132974 | 2 |
| #27132706 | 2 |
| #27132699 | 2 |
| #27132668 | 2 |
| C2×#20259243 | 2 |
| #27132630 | 2 |
| #535×C191 | 2 |
| #3096 | 191 |