Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20259369 | C2 | semidirect |
| 2. #20259353 | C2 | semidirect |
| 3. #20259352 | C2 | semidirect |
| 4. #20259342 | C2 | semidirect |
| 5. C2×#15690277 | C2 | semidirect |
| 6. #20259329 | C2 | semidirect |
| 7. 2−1+4×C191 | C2 | semidirect |
| 52. C191 | #578 | semidirect |
| 55. 2−1+4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259369 | 2 |
| #20259353 | 2 |
| #20259352 | 2 |
| #20259342 | 2 |
| C2×#15690277 | 2 |
| #20259329 | 2 |
| 2−1+4×C191 | 2 |
| #578 | 191 |