Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×D1528 | C2 | semidirect |
| 2. C2×#20259328 | C2 | semidirect |
| 3. #27133232 | C2 | semidirect |
| 4. #27132917 | C2 | semidirect |
| 5. #27132900 | C2 | semidirect |
| 6. #27132667 | C2 | semidirect |
| 7. #427×C191 | C2 | semidirect |
| 15. C2×#15690270 | C22 | semidirect |
| 16. C2×C8×D191 | C22 | semidirect |
| 19. #20259297 | C22 | semidirect |
| 21. #20259242 | C22 | semidirect |
| 24. #107×C191 | C22 | semidirect |
| 25. #106×C191 | C22 | semidirect |
| 46. C2×C8×C191 | D4 | semidirect |
| 93. C191 | #3058 | semidirect |
| 100. #427 | D191 | semidirect |
| 117. #107 | C2×D191 | semidirect |
| 118. #106 | C2×D191 | semidirect |
| 139. C2×C8 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1528 | 2 |
| C2×#20259328 | 2 |
| #27133232 | 2 |
| #27132917 | 2 |
| #27132900 | 2 |
| #27132667 | 2 |
| #427×C191 | 2 |
| #3058 | 191 |