Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14271963 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. #14271732 | C2 | semidirect |
| 4. #14271179 | C2 | semidirect |
| 5. #14271169 | C2 | semidirect |
| 6. #14271136 | C2 | semidirect |
| 7. C29×#344 | C2 | semidirect |
| 51. C2×D116 | D4 | semidirect |
| 55. C2×Dic58 | D4 | semidirect |
| 59. M16×C29 | D4 | semidirect |
| 61. C2×C8×C29 | D4 | semidirect |
| 142. #344 | D29 | semidirect |
| 173. C29 | #2008 | semidirect |
| 208. M16 | D116 | semidirect |
| 210. C2×C8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| C2×#11745270 | 2 |
| #14271732 | 2 |
| #14271179 | 2 |
| #14271169 | 2 |
| #14271136 | 2 |
| C29×#344 | 2 |
| #2008 | 29 |