Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #27133146 | C2 | semidirect |
| 3. #27132669 | C2 | semidirect |
| 4. #27132665 | C2 | semidirect |
| 5. #27132660 | C2 | semidirect |
| 6. C2×#20259244 | C2 | semidirect |
| 7. C2×#131×C191 | C2 | semidirect |
| 9. #20259368 | C4 | semidirect |
| 16. #20259281 | C22 | semidirect |
| 17. C2×C4⋊Dic191 | C22 | semidirect |
| 18. #20259247 | C22 | semidirect |
| 19. #20259247 | C22 | semidirect |
| 20. #20259244 | C22 | semidirect |
| 21. #20259244 | C22 | semidirect |
| 22. #20259244 | C22 | semidirect |
| 25. C2×M16×C191 | C22 | semidirect |
| 26. C22×C8×C191 | C22 | semidirect |
| 30. #15690287 | C2×C4 | semidirect |
| 34. C2×D764 | C2×C4 | semidirect |
| 97. C191 | #2897 | semidirect |
| 100. C2×#131 | D191 | semidirect |
| 114. C2×M16 | C2×D191 | semidirect |
| 115. C22×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259368 | 2 |
| #27133146 | 2 |
| #27132669 | 2 |
| #27132665 | 2 |
| #27132660 | 2 |
| C2×#20259244 | 2 |
| C2×#131×C191 | 2 |
| #2897 | 191 |