Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C4×Dic386 | C2 | semidirect |
| 3. #20259832 | C2 | semidirect |
| 4. #20259822 | C2 | semidirect |
| 6. #20259810 | C2 | semidirect |
| 9. #15690543 | C4 | semidirect |
| 21. Dic386 | C2×C4 | semidirect |
| 25. #13095393 | C2×C4 | semidirect |
| 49. C193 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690543 | 2 |
| C4×Dic386 | 2 |
| #20259832 | 2 |
| #20259822 | 2 |
| #20259820 | 2 |
| #20259810 | 2 |
| C4×D4×C193 | 2 |
| #440 | 193 |