Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15690277 | C2 | semidirect |
| 4. #27132902 | C2 | direct (N × H) |
| 5. C2×#20259255 | C2 | semidirect |
| 6. C2×#20259246 | C2 | semidirect |
| 7. C2×#20259245 | C2 | semidirect |
| 11. C2×#15690277 | C22 | semidirect |
| 21. #20259255 | C22 | semidirect |
| 22. #20259246 | C22 | semidirect |
| 23. #20259245 | C22 | semidirect |
| 75. C23×C191 | Q16 | semidirect |
| 99. C22×C191 | C2×Q16 | semidirect |
| 111. C2×C191 | #467 | semidirect |
| 115. C191 | C2×#467 | semidirect |
| 182. C23 | #15690277 | semidirect |
| 215. C22 | C2×#15690277 | semidirect |
| 227. C2 | #27132902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690277 | 2 |
| C23×C191⋊C8 | 2 |
| C2×#20259301 | 2 |
| #27132902 | 2 |
| C2×#20259255 | 2 |
| C2×#20259246 | 2 |
| C2×#20259245 | 2 |
| C2×C22⋊Q8×C191 | 2 |
| C2×#467 | 191 |