Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. Q8×Dic191 | C2 | semidirect |
| 4. Dic191⋊C8 | C2 | semidirect |
| 5. #20259246 | C2 | semidirect |
| 7. C2×Q16×C191 | C2 | semidirect |
| 51. C191 | #464 | semidirect |
| 53. C2×Q16 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690274 | 2 |
| #20259311 | 2 |
| Q8×Dic191 | 2 |
| Dic191⋊C8 | 2 |
| #20259246 | 2 |
| #20259244 | 2 |
| C2×Q16×C191 | 2 |
| #464 | 191 |