Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15690275 | C2 | semidirect |
| 2. C2×#20259301 | C2 | semidirect |
| 3. #27132814 | C2 | direct (N × H) |
| 4. C2×#20259243 | C2 | semidirect |
| 5. C2×C22⋊(C191⋊C8) | C2 | semidirect |
| 7. C22×Dic382 | C22 | semidirect |
| 9. C2×#15690275 | C22 | semidirect |
| 10. C22×C191⋊C8 | C22 | semidirect |
| 12. #20259301 | C22 | semidirect |
| 13. C2×C4⋊Dic191 | C22 | semidirect |
| 16. #20259243 | C22 | semidirect |
| 17. C22⋊(C191⋊C8) | C22 | semidirect |
| 27. C2×Dic382 | C23 | semidirect |
| 32. C2×C191⋊C8 | C23 | semidirect |
| 34. C4⋊Dic191 | C23 | semidirect |
| 73. C23×C191 | SD16 | semidirect |
| 97. C22×C191 | C2×SD16 | semidirect |
| 107. C2×C191 | #450 | semidirect |
| 111. C191 | C2×#450 | semidirect |
| 178. C23 | #15690275 | semidirect |
| 209. C22 | C2×#15690275 | semidirect |
| 219. C2 | #27132814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| C2×#20259301 | 2 |
| #27132814 | 2 |
| C2×#20259243 | 2 |
| C2×C22⋊(C191⋊C8) | 2 |
| C23×D4×C191 | 2 |
| C2×#450 | 191 |