Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#20259353 | C2 | semidirect |
| 3. C4×#15690287 | C2 | semidirect |
| 4. #27132882 | C2 | semidirect |
| 5. #27132875 | C2 | semidirect |
| 6. #27132687 | C2 | semidirect |
| 7. #27132672 | C2 | semidirect |
| 8. #27132668 | C2 | semidirect |
| 9. C2×#124×C191 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 15. C2×#15690274 | C22 | semidirect |
| 19. C4×Dic382 | C22 | semidirect |
| 20. C4×D764 | C22 | semidirect |
| 25. C4⋊(C191⋊C8) | C22 | semidirect |
| 26. #20259246 | C22 | semidirect |
| 125. C191 | #3040 | semidirect |
| 129. C2×#124 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| C2×#20259348 | 2 |
| C4×#15690287 | 2 |
| #27132882 | 2 |
| #27132875 | 2 |
| #27132687 | 2 |
| #27132672 | 2 |
| #27132668 | 2 |
| C2×#124×C191 | 2 |
| #3040 | 191 |