Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20259858 | C2 | semidirect |
| 3. #20259813 | C2 | semidirect |
| 4. #117×C193 | C2 | semidirect |
| 9. C2×Dic386 | C4 | semidirect |
| 10. C2×D772 | C4 | semidirect |
| 12. C2×C4×D193 | C4 | semidirect |
| 57. C193 | #410 | semidirect |
| 61. #117 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| #20259858 | 2 |
| #20259813 | 2 |
| #117×C193 | 2 |
| #410 | 193 |