Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20259321 | C2 | semidirect |
| 2. #20259312 | C2 | semidirect |
| 3. #20259302 | C2 | semidirect |
| 4. #20259301 | C2 | semidirect |
| 5. #20259301 | C2 | semidirect |
| 6. #20259300 | C2 | semidirect |
| 7. #20259287 | C2 | semidirect |
| 10. C4⋊C4×D191 | C2 | semidirect |
| 11. C2×C4⋊C4×C191 | C2 | semidirect |
| 38. C22⋊D191 | Q8 | semidirect |
| 74. C191 | #554 | semidirect |
| 86. C2×C4⋊C4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259321 | 2 |
| #20259312 | 2 |
| #20259302 | 2 |
| #20259301 | 2 |
| #20259300 | 2 |
| #20259287 | 2 |
| C4×C22⋊D191 | 2 |
| C4⋊C4×D191 | 2 |
| C2×C4⋊C4×C191 | 2 |
| #554 | 191 |