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. C2×#20259328 | C2 | semidirect |
| 2. #27133230 | C2 | semidirect |
| 3. #27132913 | C2 | semidirect |
| 4. #27132896 | C2 | semidirect |
| 5. #27132701 | C2 | semidirect |
| 6. #27132668 | C2 | semidirect |
| 7. C22×D8×C191 | C2 | semidirect |
| 11. C2×#15690270 | C22 | semidirect |
| 12. C2×C8×D191 | C22 | semidirect |
| 15. #20259293 | C22 | semidirect |
| 18. #20259256 | C22 | semidirect |
| 19. #20259254 | C22 | semidirect |
| 20. #20259243 | C22 | semidirect |
| 49. C2×C8×C191 | D4 | semidirect |
| 93. C191 | #3058 | semidirect |
| 95. C22×D8 | D191 | semidirect |
| 139. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259328 | 2 |
| #27133230 | 2 |
| #27132913 | 2 |
| #27132896 | 2 |
| #27132701 | 2 |
| #27132668 | 2 |
| C22×D8×C191 | 2 |
| #3058 | 191 |