Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. Q8×Dic191 | C2 | semidirect |
| 4. #20259255 | C2 | semidirect |
| 6. #20259232 | C2 | semidirect |
| 7. #103×C191 | C2 | semidirect |
| 10. #15690274 | C4 | semidirect |
| 27. C191⋊C8 | C2×C4 | semidirect |
| 29. Q8×C191 | C2×C4 | semidirect |
| 49. C191 | #440 | semidirect |
| 55. #103 | D191 | semidirect |
| 72. Q8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690274 | 2 |
| Q8×Dic191 | 2 |
| #20259284 | 2 |
| #20259255 | 2 |
| #20259244 | 2 |
| #20259232 | 2 |
| #103×C191 | 2 |
| #440 | 191 |