Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C4×D116 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. C2×#11745169 | C2 | semidirect |
| 5. #14271065 | C2 | semidirect |
| 6. #14270926 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 21. C2×D232 | C4 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 53. C2×C8×C29 | C2×C4 | semidirect |
| 84. C2×C4×C29 | D8 | semidirect |
| 104. D116 | C22⋊C4 | semidirect |
| 144. #336 | D29 | semidirect |
| 172. C29 | #1879 | semidirect |
| 201. C2×C8 | C4×D29 | semidirect |
| 246. C2×C4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×C4×D116 | 2 |
| C2×#11745169 | 2 |
| #14271065 | 2 |
| #14270926 | 2 |
| C29×#336 | 2 |
| #1879 | 29 |