Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×Dic386 | C2 | semidirect |
| 4. #20259833 | C2 | semidirect |
| 5. #20259824 | C2 | semidirect |
| 7. #97×C193 | C2 | semidirect |
| 11. #15690544 | C4 | semidirect |
| 22. Dic386 | C2×C4 | semidirect |
| 33. C8×C193 | C2×C4 | semidirect |
| 49. C193 | #440 | semidirect |
| 57. #97 | D193 | semidirect |
| 83. C8 | C4×D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690544 | 2 |
| C4×Dic386 | 2 |
| C4×D772 | 2 |
| #20259833 | 2 |
| #20259824 | 2 |
| #20259821 | 2 |
| #97×C193 | 2 |
| #440 | 193 |