Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259350 | C2 | semidirect |
| 2. C2×#20259319 | C2 | semidirect |
| 3. C4×#15690287 | C2 | semidirect |
| 4. #27132864 | C2 | semidirect |
| 5. #27132859 | C2 | semidirect |
| 6. #27132669 | C2 | semidirect |
| 7. #423×C191 | C2 | semidirect |
| 12. C2×#15690276 | C22 | semidirect |
| 13. C2×D1528 | C22 | semidirect |
| 17. C4×Dic382 | C22 | semidirect |
| 18. C4×D764 | C22 | semidirect |
| 23. #20259244 | C22 | semidirect |
| 26. C4⋊C8×C191 | C22 | semidirect |
| 29. #15690287 | D4 | semidirect |
| 62. Dic382 | C2×D4 | semidirect |
| 69. D764 | C2×D4 | semidirect |
| 94. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 104. C191 | #3038 | semidirect |
| 111. #423 | D191 | semidirect |
| 130. C4⋊C8 | C2×D191 | semidirect |
| 201. C4 | #20259350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259350 | 2 |
| C2×#20259319 | 2 |
| C4×#15690287 | 2 |
| #27132864 | 2 |
| #27132859 | 2 |
| #27132669 | 2 |
| #423×C191 | 2 |
| #3038 | 191 |