Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#15690544 | C2 | semidirect |
| 2. C2×#15690543 | C2 | semidirect |
| 3. C2×#15690540 | C2 | semidirect |
| 4. #20259895 | C2 | semidirect |
| 5. #20259886 | C2 | semidirect |
| 6. #20259809 | C2 | semidirect |
| 7. C2×D8×C193 | C2 | semidirect |
| 29. #13095393 | D4 | semidirect |
| 37. C8×C193 | D4 | semidirect |
| 54. C193 | #496 | semidirect |
| 59. C2×D8 | D193 | semidirect |
| 92. C8 | C22⋊D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690544 | 2 |
| C2×#15690543 | 2 |
| C2×#15690540 | 2 |
| #20259895 | 2 |
| #20259886 | 2 |
| #20259809 | 2 |
| C2×D8×C193 | 2 |
| #496 | 193 |