Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27133197 | C2 | semidirect |
| 2. #27132993 | C2 | semidirect |
| 3. #27132976 | C2 | semidirect |
| 4. #27132963 | C2 | semidirect |
| 5. #27132878 | C2 | semidirect |
| 6. #27132814 | C2 | semidirect |
| 8. #27132773 | C2 | semidirect |
| 9. #27132763 | C2 | semidirect |
| 10. #27132720 | C2 | semidirect |
| 11. C2×C4×D4×C191 | C2 | semidirect |
| 15. #20259314 | C22 | semidirect |
| 16. #20259310 | C22 | semidirect |
| 20. C4×Dic382 | C22 | semidirect |
| 21. C4×D764 | C22 | semidirect |
| 24. #20259255 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. C4⋊(C191⋊C8) | C22 | semidirect |
| 27. #20259245 | C22 | semidirect |
| 30. #20259242 | C22 | semidirect |
| 33. #20259233 | C22 | semidirect |
| 140. C191 | #3114 | semidirect |
| 143. C2×C4×D4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| #27132993 | 2 |
| #27132976 | 2 |
| #27132963 | 2 |
| #27132878 | 2 |
| #27132814 | 2 |
| #27132797 | 2 |
| #27132773 | 2 |
| #27132763 | 2 |
| #27132720 | 2 |
| C2×C4×D4×C191 | 2 |
| #3114 | 191 |