Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 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×#15690274 | C2 | semidirect |
| 3. C4×D764 | C2 | semidirect |
| 4. C4⋊(C191⋊C8) | C2 | semidirect |
| 5. #20259246 | C2 | semidirect |
| 6. #20259243 | C2 | semidirect |
| 7. #124×C191 | C2 | semidirect |
| 55. C191 | #463 | semidirect |
| 59. #124 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690274 | 2 |
| C2×#15690272 | 2 |
| C4×D764 | 2 |
| C4⋊(C191⋊C8) | 2 |
| #20259246 | 2 |
| #20259243 | 2 |
| #124×C191 | 2 |
| #463 | 191 |