Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271708 | C2 | semidirect |
| 2. #14271567 | C2 | semidirect |
| 3. #14271538 | C2 | semidirect |
| 4. #14271508 | C2 | semidirect |
| 5. #14271399 | C2 | semidirect |
| 6. #14271397 | C2 | semidirect |
| 7. D8×Dic29 | C2 | semidirect |
| 8. #14271245 | C2 | semidirect |
| 9. #14271243 | C2 | semidirect |
| 10. C2×C8×Dic29 | C2 | semidirect |
| 11. C29×#466 | C2 | semidirect |
| 89. C2×Dic29 | D8 | semidirect |
| 99. C8×C29 | #41 | semidirect |
| 101. #6597 | #41 | semidirect |
| 128. #466 | D29 | semidirect |
| 166. C29 | #3169 | semidirect |
| 229. C8 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271708 | 2 |
| #14271567 | 2 |
| #14271538 | 2 |
| #14271508 | 2 |
| #14271399 | 2 |
| #14271397 | 2 |
| D8×Dic29 | 2 |
| #14271245 | 2 |
| #14271243 | 2 |
| C2×C8×Dic29 | 2 |
| C29×#466 | 2 |
| #3169 | 29 |