Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #14271038 | C2 | semidirect |
| 5. #14271035 | C2 | semidirect |
| 6. #14270929 | C2 | semidirect |
| 7. C29×#342 | C2 | semidirect |
| 27. #11745154 | C4 | semidirect |
| 55. C22⋊C4×C29 | C2×C4 | semidirect |
| 59. C22⋊Dic29 | C2×C4 | semidirect |
| 82. C22×D29 | C4⋊C4 | semidirect |
| 113. C2×Dic29 | C4⋊C4 | semidirect |
| 154. #342 | D29 | semidirect |
| 185. C29 | #1867 | semidirect |
| 224. C22⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271636 | 2 |
| C2×#11745154 | 2 |
| #14271040 | 2 |
| #14271038 | 2 |
| #14271035 | 2 |
| #14270929 | 2 |
| C29×#342 | 2 |
| #1867 | 29 |