Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #20259315 | C2 | semidirect |
| 2. #20259315 | C2 | semidirect |
| 3. #20259308 | C2 | semidirect |
| 4. #20259306 | C2 | semidirect |
| 5. #20259305 | C2 | semidirect |
| 6. #20259304 | C2 | semidirect |
| 7. #20259301 | C2 | semidirect |
| 8. #20259299 | C2 | semidirect |
| 10. C4×C22⋊D191 | C2 | semidirect |
| 11. (C22⋊D191)⋊C4 | C2 | semidirect |
| 12. #20259281 | C2 | semidirect |
| 13. #20259278 | C2 | semidirect |
| 14. C2×C22⋊Dic191 | C2 | semidirect |
| 15. C2×C22⋊C4×C191 | C2 | semidirect |
| 16. C2×Dic382 | C22 | semidirect |
| 22. C2×C4×D191 | C22 | semidirect |
| 23. C4⋊Dic191 | C22 | semidirect |
| 24. C4⋊Dic191 | C22 | semidirect |
| 25. C4⋊Dic191 | C22 | semidirect |
| 26. Dic191⋊C4 | C22 | semidirect |
| 27. Dic191⋊C4 | C22 | semidirect |
| 28. Dic191⋊C4 | C22 | semidirect |
| 29. Dic191⋊C4 | C22 | semidirect |
| 30. Dic191⋊C4 | C22 | semidirect |
| 38. (C2×D191)⋊C4 | C22 | semidirect |
| 39. (C2×D191)⋊C4 | C22 | semidirect |
| 40. (C2×D191)⋊C4 | C22 | semidirect |
| 41. C4×Dic191 | C22 | semidirect |
| 42. C4×Dic191 | C22 | semidirect |
| 43. C4×Dic191 | C22 | semidirect |
| 110. C191 | #551 | semidirect |
| 126. C2×C22⋊C4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259315 | 2 |
| #20259308 | 2 |
| #20259306 | 2 |
| #20259305 | 2 |
| #20259304 | 2 |
| #20259301 | 2 |
| #20259299 | 2 |
| #20259291 | 2 |
| C4×C22⋊D191 | 2 |
| (C22⋊D191)⋊C4 | 2 |
| #20259281 | 2 |
| #20259278 | 2 |
| C2×C22⋊Dic191 | 2 |
| C2×C22⋊C4×C191 | 2 |
| #551 | 191 |