Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272173 | C2 | semidirect |
| 2. #14272162 | C2 | semidirect |
| 3. #14272161 | C2 | semidirect |
| 4. #14272144 | C2 | semidirect |
| 5. #14272143 | C2 | semidirect |
| 6. #14272126 | C2 | semidirect |
| 14. C2×SD16×C29 | C4 | semidirect |
| 15. C2×#90785 | C4 | semidirect |
| 16. C2×#90782 | C4 | semidirect |
| 21. C2×#90773 | C4 | semidirect |
| 148. C2×SD16 | #1181 | semidirect |
| 163. C29 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272173 | 2 |
| #14272162 | 2 |
| #14272161 | 2 |
| #14272144 | 2 |
| #14272143 | 2 |
| #14272126 | 2 |
| C2×#11745278 | 2 |
| #1976 | 29 |