Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
696 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C4×#90779 | C2 | semidirect |
| 4. #14271014 | C2 | semidirect |
| 14. C2×#90779 | C4 | semidirect |
| 21. #11745239 | C4 | semidirect |
| 43. #90779 | C2×C4 | semidirect |
| 46. C4×Dic29 | C2×C4 | semidirect |
| 64. C2×Dic29 | C42 | semidirect |
| 114. C29 | #2274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745239 | 2 |
| C22×#90779 | 2 |
| C4×#90779 | 2 |
| #14271014 | 2 |
| C22⋊C4×Dic29 | 2 |
| C4×C22⋊Dic29 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2274 | 29 |