Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133174 | C2 | semidirect |
| 2. #27132998 | C2 | semidirect |
| 3. #27132984 | C2 | semidirect |
| 4. #27132981 | C2 | semidirect |
| 5. #27132897 | C2 | semidirect |
| 6. #27132890 | C2 | semidirect |
| 7. #27132814 | C2 | semidirect |
| 8. #27132806 | C2 | semidirect |
| 9. #27132797 | C2 | semidirect |
| 10. C2×C22⋊(C191⋊C8) | C2 | semidirect |
| 11. C2×#121×C191 | C2 | semidirect |
| 12. C2×#15690287 | C22 | semidirect |
| 13. C2×#15690275 | C22 | semidirect |
| 14. C2×#15690272 | C22 | semidirect |
| 15. C22×C191⋊C8 | C22 | semidirect |
| 18. #20259301 | C22 | semidirect |
| 20. #20259296 | C22 | semidirect |
| 24. #20259281 | C22 | semidirect |
| 25. #20259255 | C22 | semidirect |
| 26. #20259253 | C22 | semidirect |
| 27. #20259245 | C22 | semidirect |
| 28. #20259243 | C22 | semidirect |
| 29. #20259243 | C22 | semidirect |
| 30. #20259242 | C22 | semidirect |
| 33. C22⋊(C191⋊C8) | C22 | semidirect |
| 158. C191 | #3188 | semidirect |
| 161. C2×#121 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133174 | 2 |
| #27132998 | 2 |
| #27132984 | 2 |
| #27132981 | 2 |
| #27132897 | 2 |
| #27132890 | 2 |
| #27132814 | 2 |
| #27132806 | 2 |
| #27132797 | 2 |
| C2×C22⋊(C191⋊C8) | 2 |
| C2×#121×C191 | 2 |
| #3188 | 191 |