Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×C4⋊Dic29 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. #14270926 | C2 | semidirect |
| 5. C2×C29×C22⋊C8 | C2 | semidirect |
| 12. #11745292 | C4 | semidirect |
| 39. C2×D116 | C2×C4 | semidirect |
| 47. C4⋊Dic29 | C2×C4 | semidirect |
| 48. C4⋊Dic29 | D4 | semidirect |
| 91. C22×C29 | #102 | semidirect |
| 114. C2×C22⋊C8 | D29 | semidirect |
| 139. C29 | #1874 | semidirect |
| 217. C22 | #11745169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| C22×C4⋊Dic29 | 2 |
| C2×#11745169 | 2 |
| #14270926 | 2 |
| C2×C29×C22⋊C8 | 2 |
| #1874 | 29 |