Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14271280 | C2 | semidirect |
| 2. #14270993 | C2 | semidirect |
| 3. #14270970 | C2 | semidirect |
| 4. C16×Dic29 | C2 | semidirect |
| 8. C29×Q32 | C4 | semidirect |
| 9. C29×SD32 | C4 | semidirect |
| 10. C29×D16 | C4 | semidirect |
| 57. Q32 | Dic29 | semidirect |
| 58. SD32 | Dic29 | semidirect |
| 59. D16 | Dic29 | semidirect |
| 65. C29 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271280 | 2 |
| #14270993 | 2 |
| #14270970 | 2 |
| C16×Dic29 | 2 |
| C29×#508 | 2 |
| #2178 | 29 |