Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 4. C4⋊#13095393 | C2 | semidirect |
| 5. #20259828 | C2 | semidirect |
| 6. #20259828 | C2 | semidirect |
| 7. C4⋊C8×C193 | C2 | semidirect |
| 49. C193 | #424 | semidirect |
| 57. C4⋊C8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690538 | 2 |
| C2×C8×D193 | 2 |
| #20259856 | 2 |
| C4⋊#13095393 | 2 |
| #20259828 | 2 |
| C4⋊C8×C193 | 2 |
| #424 | 193 |