Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133234 | C2 | semidirect |
| 2. #27133004 | C2 | semidirect |
| 3. #27132984 | C2 | semidirect |
| 4. #27132907 | C2 | semidirect |
| 5. #27132890 | C2 | semidirect |
| 6. #27132814 | C2 | semidirect |
| 7. #27132801 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 10. C22×Dic382 | C22 | semidirect |
| 13. C2×#15690271 | C22 | semidirect |
| 14. C22×C191⋊C8 | C22 | semidirect |
| 20. #20259301 | C22 | semidirect |
| 21. #20259281 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259253 | C22 | semidirect |
| 24. #20259245 | C22 | semidirect |
| 25. #20259245 | C22 | semidirect |
| 29. C22⋊(C191⋊C8) | C22 | semidirect |
| 137. C191 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133234 | 2 |
| #27133004 | 2 |
| #27132984 | 2 |
| #27132907 | 2 |
| #27132890 | 2 |
| #27132814 | 2 |
| #27132801 | 2 |
| #27132630 | 2 |
| #535×C191 | 2 |
| #3200 | 191 |