Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #27132996 | C2 | semidirect |
| 3. #27132976 | C2 | semidirect |
| 4. #27132911 | C2 | semidirect |
| 5. #27132813 | C2 | semidirect |
| 6. #27132802 | C2 | semidirect |
| 7. #27132627 | C2 | semidirect |
| 8. C2×C22⋊Q8×C191 | C2 | semidirect |
| 11. C2×#15690274 | C22 | semidirect |
| 12. C2×#15690271 | C22 | semidirect |
| 19. #20259255 | C22 | semidirect |
| 20. #20259246 | C22 | semidirect |
| 21. #20259242 | C22 | semidirect |
| 23. C22⋊(C191⋊C8) | C22 | semidirect |
| 24. C22×Q8×C191 | C22 | semidirect |
| 29. C22⋊Q8×C191 | C22 | semidirect |
| 31. C2×C4⋊C4×C191 | C22 | semidirect |
| 129. C191 | #3193 | semidirect |
| 131. C2×C22⋊Q8 | D191 | semidirect |
| 139. C22×Q8 | C2×D191 | semidirect |
| 148. C22⋊Q8 | C2×D191 | semidirect |
| 155. C2×C4⋊C4 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259296 | 2 |
| #27132996 | 2 |
| #27132976 | 2 |
| #27132911 | 2 |
| #27132813 | 2 |
| #27132802 | 2 |
| #27132627 | 2 |
| C2×C22⋊Q8×C191 | 2 |
| #3193 | 191 |