Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 144 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. #14272195 | C2 | semidirect |
| 2. #14272194 | C2 | semidirect |
| 3. #14272193 | C2 | semidirect |
| 4. #14272192 | C2 | semidirect |
| 5. #14272184 | C2 | semidirect |
| 6. #14272183 | C2 | semidirect |
| 7. #14272137 | C2 | semidirect |
| 8. #14272136 | C2 | semidirect |
| 160. C29 | #2980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272195 | 2 |
| #14272194 | 2 |
| #14272193 | 2 |
| #14272192 | 2 |
| #14272184 | 2 |
| #14272183 | 2 |
| #14272137 | 2 |
| #14272136 | 2 |
| #14271708 | 2 |
| #2980 | 29 |