Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 48 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. #20259978 | C2 | semidirect |
| 2. #20259958 | C2 | semidirect |
| 3. #20259957 | C2 | semidirect |
| 10. C2×Dic386 | C4 | semidirect |
| 12. C2×C22⋊D193 | C4 | semidirect |
| 14. C2×C4×D193 | C4 | semidirect |
| 16. C22×C4×C193 | C4 | semidirect |
| 53. C193 | #410 | semidirect |
| 67. C22×C4 | #11715871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259978 | 2 |
| #20259958 | 2 |
| #20259957 | 2 |
| C2×#15690555 | 2 |
| #410 | 193 |