Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #14271636 | C2 | semidirect |
| 3. C2×#11745154 | C2 | semidirect |
| 4. C2×#11745154 | C2 | semidirect |
| 5. C2×#11745154 | C2 | semidirect |
| 6. #14270929 | C2 | semidirect |
| 7. C29×#342 | C2 | semidirect |
| 18. #11745248 | C4 | semidirect |
| 20. #11745244 | C4 | semidirect |
| 28. C23×D29 | C2×C4 | semidirect |
| 47. C22×Dic29 | C2×C4 | semidirect |
| 55. C22⋊C4×C29 | C2×C4 | semidirect |
| 56. C22⋊C4×C29 | D4 | semidirect |
| 60. C22⋊Dic29 | D4 | semidirect |
| 145. #342 | D29 | semidirect |
| 175. C29 | #1913 | semidirect |
| 213. C22⋊C4 | C4×D29 | semidirect |
| 214. C22⋊C4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271725 | 2 |
| #14271636 | 2 |
| C2×#11745154 | 2 |
| #14270929 | 2 |
| C29×#342 | 2 |
| #1913 | 29 |