Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 189 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. #14271290 | C2 | semidirect |
| 3. #14271287 | C2 | semidirect |
| 37. C2×#6597 | Q8 | semidirect |
| 90. C29 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271290 | 2 |
| #14271287 | 2 |
| #14271191 | 2 |
| #14271121 | 2 |
| C2×C4×#6597 | 2 |
| C29×#423 | 2 |
| #2960 | 29 |