Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#15690276 | C2 | semidirect |
| 2. C2×#15690275 | C2 | semidirect |
| 3. C2×#15690274 | C2 | semidirect |
| 4. #20259320 | C2 | semidirect |
| 6. C8×Dic191 | C2 | semidirect |
| 7. C2×SD16×C191 | C2 | semidirect |
| 29. C191⋊C8 | D4 | semidirect |
| 37. C8×C191 | D4 | semidirect |
| 47. Dic191 | SD16 | semidirect |
| 52. C191 | #492 | semidirect |
| 57. C2×SD16 | D191 | semidirect |
| 90. C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690276 | 2 |
| C2×#15690275 | 2 |
| C2×#15690274 | 2 |
| #20259320 | 2 |
| #20259318 | 2 |
| C8×Dic191 | 2 |
| C2×SD16×C191 | 2 |
| #492 | 191 |