Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20259302 | C2 | semidirect |
| 2. #20259301 | C2 | semidirect |
| 3. #20259300 | C2 | semidirect |
| 4. #20259300 | C2 | semidirect |
| 5. #20259299 | C2 | semidirect |
| 6. #20259298 | C2 | semidirect |
| 9. C22⋊Q8×C191 | C2 | semidirect |
| 11. C2×Dic382 | C22 | semidirect |
| 12. C2×Dic382 | C22 | semidirect |
| 16. C4⋊Dic191 | C22 | semidirect |
| 17. C4⋊Dic191 | C22 | semidirect |
| 18. Dic191⋊C4 | C22 | semidirect |
| 19. Dic191⋊C4 | C22 | semidirect |
| 20. Dic191⋊C4 | C22 | semidirect |
| 26. C2×Q8×C191 | C22 | semidirect |
| 28. C4⋊C4×C191 | C22 | semidirect |
| 29. C4⋊C4×C191 | C22 | semidirect |
| 33. C22×D191 | Q8 | semidirect |
| 70. C191 | #543 | semidirect |
| 78. C22⋊Q8 | D191 | semidirect |
| 84. C2×Q8 | C2×D191 | semidirect |
| 94. C4⋊C4 | C2×D191 | semidirect |
| 95. C4⋊C4 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259302 | 2 |
| #20259301 | 2 |
| #20259300 | 2 |
| #20259299 | 2 |
| #20259298 | 2 |
| C2×(C2×D191)⋊C4 | 2 |
| C22⋊C4×D191 | 2 |
| C22⋊Q8×C191 | 2 |
| #543 | 191 |