Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×C8×D29 | C2 | semidirect |
| 3. C2×#11745168 | C2 | semidirect |
| 4. C2×#11745168 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 36. C2×D116 | C8 | semidirect |
| 54. C2×C8×C29 | D4 | semidirect |
| 65. C2×#6597 | D4 | semidirect |
| 80. C22×D29 | C2×C8 | semidirect |
| 87. C2×C4×C29 | C2×C8 | semidirect |
| 134. C2×D29 | C22⋊C8 | semidirect |
| 149. #336 | D29 | semidirect |
| 178. C29 | #1869 | semidirect |
| 213. C2×C8 | D116 | semidirect |
| 254. C2×C4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×C4×D116 | 2 |
| C2×#11745168 | 2 |
| #14270918 | 2 |
| C29×#336 | 2 |
| #1869 | 29 |