Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #27133001 | C2 | semidirect |
| 3. #27132993 | C2 | semidirect |
| 4. #27132976 | C2 | semidirect |
| 5. #27132902 | C2 | semidirect |
| 6. #27132894 | C2 | semidirect |
| 7. #27132823 | C2 | semidirect |
| 8. #27132819 | C2 | semidirect |
| 9. #27132802 | C2 | semidirect |
| 10. C2×C22⋊(C191⋊C8) | C2 | semidirect |
| 11. C2×C22⋊Q8×C191 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 14. C2×#15690274 | C22 | semidirect |
| 25. #20259255 | C22 | semidirect |
| 26. #20259253 | C22 | semidirect |
| 27. #20259246 | C22 | semidirect |
| 28. #20259246 | C22 | semidirect |
| 29. #20259245 | C22 | semidirect |
| 30. #20259242 | C22 | semidirect |
| 149. C191 | #3190 | semidirect |
| 152. C2×C22⋊Q8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133174 | 2 |
| #27133001 | 2 |
| #27132993 | 2 |
| #27132976 | 2 |
| #27132902 | 2 |
| #27132894 | 2 |
| #27132823 | 2 |
| #27132819 | 2 |
| #27132802 | 2 |
| C2×C22⋊(C191⋊C8) | 2 |
| C2×C22⋊Q8×C191 | 2 |
| #3190 | 191 |