Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20259897 | C2 | semidirect |
| 3. #20259889 | C2 | semidirect |
| 6. Q8×Dic193 | C2 | semidirect |
| 7. #20259864 | C2 | semidirect |
| 8. #20259864 | C2 | semidirect |
| 38. C2×Dic193 | Q8 | semidirect |
| 70. C193 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259898 | 2 |
| #20259897 | 2 |
| #20259889 | 2 |
| #20259878 | 2 |
| #20259876 | 2 |
| Q8×Dic193 | 2 |
| #20259864 | 2 |
| #20259855 | 2 |
| C2×C4×Dic193 | 2 |
| C22⋊Q8×C193 | 2 |
| #533 | 193 |