Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14272167 | C2 | semidirect |
| 2. C2×#11745226 | C2 | semidirect |
| 3. C42×#1181 | C2 | semidirect |
| 9. C29×C4⋊Q8 | C4 | semidirect |
| 10. #11745309 | C4 | semidirect |
| 13. #11745236 | C4 | semidirect |
| 30. C4×#1181 | D4 | semidirect |
| 64. C4×C29 | #104 | semidirect |
| 79. C4⋊Q8 | #1181 | semidirect |
| 89. C29 | #1962 | semidirect |
| 139. C4 | #11745226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272167 | 2 |
| C2×#11745226 | 2 |
| C42×#1181 | 2 |
| #14271714 | 2 |
| #1962 | 29 |