Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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. #14272213 | C2 | semidirect |
| 3. #14272212 | C2 | semidirect |
| 40. #90796 | Q8 | semidirect |
| 120. C29 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| #14272213 | 2 |
| #14272212 | 2 |
| #14272170 | 2 |
| D29⋊(C4⋊C8) | 2 |
| #14272128 | 2 |
| C4×#90796 | 2 |
| #14271718 | 2 |
| #2962 | 29 |