Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133045 | C2 | semidirect |
| 3. #27133017 | C2 | semidirect |
| 4. #27132882 | C2 | semidirect |
| 5. #27132875 | C2 | semidirect |
| 6. #27132819 | C2 | semidirect |
| 7. #27132814 | C2 | semidirect |
| 8. #27132802 | C2 | semidirect |
| 10. #27132716 | C2 | semidirect |
| 11. C2×#124×C191 | C2 | semidirect |
| 12. C2×#15690277 | C22 | semidirect |
| 14. C2×#15690274 | C22 | semidirect |
| 17. #20259314 | C22 | semidirect |
| 18. #20259310 | C22 | semidirect |
| 22. C4×Dic382 | C22 | semidirect |
| 23. C4×D764 | C22 | semidirect |
| 26. C4⋊(C191⋊C8) | C22 | semidirect |
| 27. #20259246 | C22 | semidirect |
| 28. #20259246 | C22 | semidirect |
| 33. C4×C191⋊C8 | C22 | semidirect |
| 143. C191 | #3211 | semidirect |
| 146. C2×#124 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| #27133045 | 2 |
| #27133017 | 2 |
| #27132882 | 2 |
| #27132875 | 2 |
| #27132819 | 2 |
| #27132814 | 2 |
| #27132802 | 2 |
| #27132797 | 2 |
| #27132716 | 2 |
| C2×#124×C191 | 2 |
| #3211 | 191 |