Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20259898 | C2 | semidirect |
| 2. #20259894 | C2 | semidirect |
| 3. #20259892 | C2 | semidirect |
| 5. #20259875 | C2 | semidirect |
| 6. Q8×Dic193 | C2 | semidirect |
| 7. #20259864 | C2 | semidirect |
| 9. #20259858 | C2 | semidirect |
| 10. #20259857 | C2 | semidirect |
| 11. C22⋊Q8×C193 | C2 | semidirect |
| 72. C193 | #556 | semidirect |
| 79. C22⋊Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259898 | 2 |
| #20259894 | 2 |
| #20259892 | 2 |
| #20259885 | 2 |
| #20259875 | 2 |
| Q8×Dic193 | 2 |
| #20259864 | 2 |
| C4×C22⋊D193 | 2 |
| #20259858 | 2 |
| #20259857 | 2 |
| C22⋊Q8×C193 | 2 |
| #556 | 193 |