Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 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 |
|---|---|---|
| 1. #20259355 | C2 | semidirect |
| 3. C2×#15690276 | C2 | semidirect |
| 4. #20259328 | C2 | semidirect |
| 5. #20259240 | C2 | semidirect |
| 6. #20259238 | C2 | semidirect |
| 7. #108×C191 | C2 | semidirect |
| 51. C191 | #471 | semidirect |
| 57. #108 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259355 | 2 |
| #20259350 | 2 |
| C2×#15690276 | 2 |
| #20259328 | 2 |
| #20259240 | 2 |
| #20259238 | 2 |
| #108×C191 | 2 |
| #471 | 191 |