Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×Dic191 | C2 | semidirect |
| 3. #20259256 | C2 | semidirect |
| 4. #20259246 | C2 | semidirect |
| 6. #20259232 | C2 | semidirect |
| 18. SD16×C191 | C4 | semidirect |
| 28. Q8×C191 | C2×C4 | semidirect |
| 33. C8×C191 | C2×C4 | semidirect |
| 49. C191 | #440 | semidirect |
| 61. SD16 | Dic191 | semidirect |
| 72. Q8 | C2×Dic191 | semidirect |
| 83. C8 | C2×Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic191 | 2 |
| D4×Dic191 | 2 |
| #20259256 | 2 |
| #20259246 | 2 |
| #20259243 | 2 |
| #20259232 | 2 |
| C2×SD16×C191 | 2 |
| #440 | 191 |