Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20259317 | C2 | semidirect |
| 2. #20259313 | C2 | semidirect |
| 3. #20259313 | C2 | semidirect |
| 5. #20259298 | C2 | semidirect |
| 6. Q8×Dic191 | C2 | semidirect |
| 8. #20259280 | C2 | semidirect |
| 9. #20259278 | C2 | semidirect |
| 10. C2×C4⋊Dic191 | C2 | semidirect |
| 11. C22⋊Q8×C191 | C2 | semidirect |
| 72. C191 | #552 | semidirect |
| 79. C22⋊Q8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259317 | 2 |
| #20259313 | 2 |
| #20259306 | 2 |
| #20259298 | 2 |
| Q8×Dic191 | 2 |
| C4×C22⋊D191 | 2 |
| #20259280 | 2 |
| #20259278 | 2 |
| C2×C4⋊Dic191 | 2 |
| C22⋊Q8×C191 | 2 |
| #552 | 191 |