Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20259367 | C2 | semidirect |
| 2. #20259348 | C2 | semidirect |
| 3. #20259346 | C2 | semidirect |
| 4. #20259344 | C2 | semidirect |
| 5. #20259341 | C2 | semidirect |
| 6. D8×D191 | C2 | semidirect |
| 7. #20259328 | C2 | semidirect |
| 8. C2×D8×C191 | C2 | semidirect |
| 10. #15690287 | C22 | semidirect |
| 12. #15690286 | C22 | semidirect |
| 15. D4×D191 | C22 | semidirect |
| 16. Dic764 | C22 | semidirect |
| 17. #15690276 | C22 | semidirect |
| 18. #15690275 | C22 | semidirect |
| 19. D1528 | C22 | semidirect |
| 20. #15690272 | C22 | semidirect |
| 21. #15690271 | C22 | semidirect |
| 22. #15690270 | C22 | semidirect |
| 23. C8×D191 | C22 | semidirect |
| 24. C2×D4×C191 | C22 | semidirect |
| 25. D8×C191 | C22 | semidirect |
| 26. D8×C191 | C22 | semidirect |
| 27. C2×C8×C191 | C22 | semidirect |
| 62. C191 | #576 | semidirect |
| 70. C2×D8 | D191 | semidirect |
| 79. C2×D4 | C2×D191 | semidirect |
| 85. D8 | C2×D191 | semidirect |
| 86. D8 | C2×D191 | semidirect |
| 90. C2×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259367 | 2 |
| #20259348 | 2 |
| #20259346 | 2 |
| #20259344 | 2 |
| #20259341 | 2 |
| D8×D191 | 2 |
| #20259328 | 2 |
| C2×D8×C191 | 2 |
| #576 | 191 |