Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#15690543 | C2 | semidirect |
| 2. C22×#13095393 | C2 | semidirect |
| 3. #20259878 | C2 | semidirect |
| 4. #20259830 | C2 | semidirect |
| 5. #20259822 | C2 | semidirect |
| 6. #20259820 | C2 | semidirect |
| 26. #13095393 | D4 | semidirect |
| 42. C22×C193 | SD16 | semidirect |
| 55. C193 | #465 | semidirect |
| 98. C22 | #15690543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690543 | 2 |
| C22×#13095393 | 2 |
| #20259878 | 2 |
| #20259830 | 2 |
| #20259822 | 2 |
| #20259820 | 2 |
| #121×C193 | 2 |
| #465 | 193 |