Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #20259328 | C2 | semidirect |
| 3. #20259257 | C2 | semidirect |
| 4. #20259249 | C2 | semidirect |
| 5. #20259248 | C2 | semidirect |
| 6. #20259232 | C2 | semidirect |
| 7. #131×C191 | C2 | semidirect |
| 9. #15690277 | C4 | semidirect |
| 10. #15690275 | C4 | semidirect |
| 11. #15690274 | C4 | semidirect |
| 12. #15690272 | C4 | semidirect |
| 51. C191 | #444 | semidirect |
| 55. #131 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259342 | 2 |
| #20259328 | 2 |
| #20259257 | 2 |
| #20259249 | 2 |
| #20259248 | 2 |
| #20259232 | 2 |
| #131×C191 | 2 |
| #444 | 191 |