Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 1. C2×#15690272 | C2 | semidirect |
| 2. C2×C8×D191 | C2 | semidirect |
| 3. #20259297 | C2 | semidirect |
| 4. #20259293 | C2 | semidirect |
| 5. #20259255 | C2 | semidirect |
| 6. #20259244 | C2 | semidirect |
| 7. #102×C191 | C2 | semidirect |
| 31. C191⋊C8 | D4 | semidirect |
| 47. C2×D191 | D8 | semidirect |
| 59. C191 | #466 | semidirect |
| 67. #102 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690272 | 2 |
| C2×C8×D191 | 2 |
| #20259297 | 2 |
| #20259293 | 2 |
| #20259255 | 2 |
| #20259244 | 2 |
| #102×C191 | 2 |
| #466 | 191 |