Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#15690534 | C2 | semidirect |
| 4. #20259806 | C2 | semidirect |
| 7. C22×Dic193 | C4 | semidirect |
| 37. C22×C193 | C4⋊C4 | semidirect |
| 46. Dic193 | C22⋊C4 | semidirect |
| 53. C193 | #380 | semidirect |
| 91. C22 | #15690534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic193 | 2 |
| C2×#15690534 | 2 |
| C2×C22⋊Dic193 | 2 |
| #20259806 | 2 |
| C2×C22⋊C4×C193 | 2 |
| #380 | 193 |