Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 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. #14271751 | C2 | semidirect |
| 2. #14271316 | C2 | semidirect |
| 3. #14271299 | C2 | semidirect |
| 4. #14271072 | C2 | semidirect |
| 5. #14270901 | C2 | semidirect |
| 6. #14270898 | C2 | semidirect |
| 7. C29×#323 | C2 | semidirect |
| 41. C2×D116 | D4 | semidirect |
| 43. C2×Dic58 | D4 | semidirect |
| 54. C4⋊Dic29 | D4 | semidirect |
| 55. C4⋊Dic29 | D4 | semidirect |
| 134. #323 | D29 | semidirect |
| 162. C29 | #1600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271751 | 2 |
| #14271316 | 2 |
| #14271299 | 2 |
| #14271072 | 2 |
| #14270901 | 2 |
| #14270898 | 2 |
| C29×#323 | 2 |
| #1600 | 29 |