Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 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. #14272214 | C2 | semidirect |
| 2. #14272196 | C2 | semidirect |
| 3. #14272194 | C2 | semidirect |
| 4. #14272192 | C2 | semidirect |
| 5. #14272187 | C2 | semidirect |
| 6. #14272185 | C2 | semidirect |
| 7. #14272169 | C2 | semidirect |
| 8. #14272168 | C2 | semidirect |
| 151. C29 | #2995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| #14272196 | 2 |
| #14272194 | 2 |
| #14272192 | 2 |
| #14272187 | 2 |
| #14272185 | 2 |
| #14272169 | 2 |
| #14272168 | 2 |
| #14271692 | 2 |
| #2995 | 29 |