Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#15690277 | C2 | semidirect |
| 3. C2×#15690274 | C2 | semidirect |
| 4. #20259245 | C2 | semidirect |
| 5. #20259242 | C2 | semidirect |
| 6. C22⋊(C191⋊C8) | C2 | semidirect |
| 7. C22⋊Q8×C191 | C2 | semidirect |
| 60. C191 | #452 | semidirect |
| 65. C22⋊Q8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690287 | 2 |
| C2×#15690277 | 2 |
| C2×#15690274 | 2 |
| #20259245 | 2 |
| #20259242 | 2 |
| C22⋊(C191⋊C8) | 2 |
| C22⋊Q8×C191 | 2 |
| #452 | 191 |