Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20259894 | C2 | semidirect |
| 4. #20259894 | C2 | semidirect |
| 5. #20259892 | C2 | semidirect |
| 6. #20259892 | C2 | semidirect |
| 7. #20259890 | C2 | semidirect |
| 8. #20259889 | C2 | semidirect |
| 12. #20259878 | C2 | semidirect |
| 13. #20259877 | C2 | semidirect |
| 14. #20259875 | C2 | semidirect |
| 15. C22⋊Q8×C193 | C2 | semidirect |
| 97. C193 | #563 | semidirect |
| 113. 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 |
| #20259897 | 2 |
| #20259894 | 2 |
| #20259892 | 2 |
| #20259890 | 2 |
| #20259889 | 2 |
| #20259885 | 2 |
| #20259882 | 2 |
| #20259881 | 2 |
| #20259878 | 2 |
| #20259877 | 2 |
| #20259875 | 2 |
| C22⋊Q8×C193 | 2 |
| #563 | 193 |