Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×Dic764 | C2 | semidirect |
| 2. C2×#15690277 | C2 | semidirect |
| 4. #20259320 | C2 | semidirect |
| 6. #20259232 | C2 | semidirect |
| 49. C191 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic764 | 2 |
| C2×#15690277 | 2 |
| C2×#15690275 | 2 |
| #20259320 | 2 |
| #20259309 | 2 |
| #20259232 | 2 |
| C2×SD16×C191 | 2 |
| #497 | 191 |