Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#11745174 | C2 | semidirect |
| 2. C2×C16×D29 | C2 | semidirect |
| 3. #14271400 | C2 | semidirect |
| 4. #14271396 | C2 | semidirect |
| 5. #14270988 | C2 | semidirect |
| 6. #14270965 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 39. #90768 | D4 | semidirect |
| 68. C2×D29 | D16 | semidirect |
| 80. #357 | D29 | semidirect |
| 100. C29 | #2215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| C2×C16×D29 | 2 |
| #14271400 | 2 |
| #14271396 | 2 |
| #14270988 | 2 |
| #14270965 | 2 |
| C29×#357 | 2 |
| #2215 | 29 |