Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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. #14271640 | C2 | semidirect |
| 3. #14271137 | C2 | semidirect |
| 4. #14271136 | C2 | semidirect |
| 5. #14271135 | C2 | semidirect |
| 6. C29×#410 | C2 | semidirect |
| 10. C2×Q8×D29 | C4 | semidirect |
| 11. C2×#90807 | C4 | semidirect |
| 13. C2×#90805 | C4 | semidirect |
| 15. C22×Dic58 | C4 | semidirect |
| 114. #410 | D29 | semidirect |
| 138. C29 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745365 | 2 |
| #14271640 | 2 |
| #14271137 | 2 |
| #14271136 | 2 |
| #14271135 | 2 |
| C29×#410 | 2 |
| #2884 | 29 |