Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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. #20259313 | C2 | semidirect |
| 3. #20259244 | C2 | semidirect |
| 4. #20259243 | C2 | semidirect |
| 5. #20259242 | C2 | semidirect |
| 6. #20259232 | C2 | semidirect |
| 7. #102×C191 | C2 | semidirect |
| 52. C191 | #490 | semidirect |
| 59. #102 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259318 | 2 |
| #20259313 | 2 |
| #20259244 | 2 |
| #20259243 | 2 |
| #20259242 | 2 |
| #20259232 | 2 |
| #102×C191 | 2 |
| #490 | 191 |