Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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×#15690563 | C2 | semidirect |
| 2. #20259956 | C2 | semidirect |
| 3. C22⋊#13095400 | C2 | semidirect |
| 6. C2×#13095400 | C22 | semidirect |
| 18. C22×D193 | C8 | semidirect |
| 34. C22×C193 | C2×C8 | semidirect |
| 41. C2×D193 | C2×C8 | semidirect |
| 52. D193 | C22⋊C8 | semidirect |
| 53. C193 | C2×C22⋊C8 | semidirect |
| 95. C22 | #15690563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690563 | 2 |
| #20259956 | 2 |
| C22⋊#13095400 | 2 |
| C22×C4×D193 | 2 |
| C2×C22⋊C8 | 193 |