Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14271961 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. #14270935 | C2 | semidirect |
| 7. C29×#421 | C2 | semidirect |
| 53. C2×D116 | D4 | semidirect |
| 55. C2×Dic58 | D4 | semidirect |
| 57. M16×C29 | D4 | semidirect |
| 72. C2×#6597 | D4 | semidirect |
| 139. #421 | D29 | semidirect |
| 173. C29 | #2008 | semidirect |
| 208. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| C2×#11745270 | 2 |
| #14271727 | 2 |
| #14271167 | 2 |
| #14271136 | 2 |
| #14270935 | 2 |
| C29×#421 | 2 |
| #2008 | 29 |