Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20259301 | C2 | semidirect |
| 2. #27132993 | C2 | semidirect |
| 3. #27132979 | C2 | semidirect |
| 4. #27132890 | C2 | semidirect |
| 5. #27132814 | C2 | semidirect |
| 6. #27132801 | C2 | semidirect |
| 7. C2×C22⋊(C191⋊C8) | C2 | semidirect |
| 9. C22×Dic382 | C22 | semidirect |
| 10. C2×#15690275 | C22 | semidirect |
| 11. C22×C191⋊C8 | C22 | semidirect |
| 15. #20259301 | C22 | semidirect |
| 16. C2×C4⋊Dic191 | C22 | semidirect |
| 19. #20259253 | C22 | semidirect |
| 20. #20259245 | C22 | semidirect |
| 21. #20259243 | C22 | semidirect |
| 23. C22⋊(C191⋊C8) | C22 | semidirect |
| 80. C23×C191 | SD16 | semidirect |
| 129. C191 | #3187 | semidirect |
| 203. C23 | #15690275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259301 | 2 |
| #27132993 | 2 |
| #27132979 | 2 |
| #27132890 | 2 |
| #27132814 | 2 |
| #27132801 | 2 |
| C2×C22⋊(C191⋊C8) | 2 |
| C2×#121×C191 | 2 |
| #3187 | 191 |