Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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. #20259281 | C2 | semidirect |
| 2. #20259255 | C2 | semidirect |
| 3. #20259253 | C2 | semidirect |
| 4. #20259243 | C2 | semidirect |
| 5. #20259243 | C2 | semidirect |
| 6. C22⋊(C191⋊C8) | C2 | semidirect |
| 51. C191 | #482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259281 | 2 |
| #20259255 | 2 |
| #20259253 | 2 |
| #20259243 | 2 |
| C22⋊(C191⋊C8) | 2 |
| #121×C191 | 2 |
| #482 | 191 |