Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20259317 | C2 | semidirect |
| 2. #20259313 | C2 | semidirect |
| 3. #20259312 | C2 | semidirect |
| 5. #20259302 | C2 | semidirect |
| 6. #20259301 | C2 | semidirect |
| 7. #20259287 | C2 | semidirect |
| 9. #20259281 | C2 | semidirect |
| 10. #20259280 | C2 | semidirect |
| 11. C2×C4⋊C4×C191 | C2 | semidirect |
| 72. C191 | #552 | semidirect |
| 84. C2×C4⋊C4 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259317 | 2 |
| #20259313 | 2 |
| #20259312 | 2 |
| #20259305 | 2 |
| #20259302 | 2 |
| #20259301 | 2 |
| #20259287 | 2 |
| C4×C22⋊D191 | 2 |
| #20259281 | 2 |
| #20259280 | 2 |
| C2×C4⋊C4×C191 | 2 |
| #552 | 191 |