Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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. C2×#11745306 | C2 | semidirect |
| 4. #14271070 | C2 | semidirect |
| 5. #14271068 | C2 | semidirect |
| 6. #14271058 | C2 | semidirect |
| 7. #14271032 | C2 | semidirect |
| 44. C22×Dic29 | Q8 | semidirect |
| 100. C22×C29 | C4⋊Q8 | semidirect |
| 113. Dic29 | C22⋊Q8 | semidirect |
| 150. C29 | #2857 | semidirect |
| 219. C22 | #11745306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745306 | 2 |
| C2×#11745286 | 2 |
| C22×C4×Dic29 | 2 |
| #14271070 | 2 |
| #14271068 | 2 |
| #14271058 | 2 |
| #14271032 | 2 |
| #14271021 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| #2857 | 29 |