Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#11745182 | C2 | semidirect |
| 3. C2×#11745154 | C2 | semidirect |
| 4. #14271042 | C2 | semidirect |
| 5. C29×#386 | C2 | semidirect |
| 7. C23×C4×C29 | C22 | semidirect |
| 12. #11745359 | C4 | semidirect |
| 17. C2×C22⋊C4×C29 | C22 | semidirect |
| 18. C2×C22⋊Dic29 | C22 | semidirect |
| 69. C23×C29 | C22⋊C4 | semidirect |
| 82. C22×D29 | C22⋊C4 | semidirect |
| 95. C2×C4×C29 | C22⋊C4 | semidirect |
| 107. C2×Dic29 | C22⋊C4 | semidirect |
| 144. #386 | D29 | semidirect |
| 163. C23×C4 | C2×D29 | semidirect |
| 167. C2×C22⋊C4 | C2×D29 | semidirect |
| 172. C29 | #1790 | semidirect |
| 226. C23 | #90781 | semidirect |
| 259. C2×C4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745359 | 2 |
| C2×#11745182 | 2 |
| C2×#11745154 | 2 |
| #14271042 | 2 |
| C29×#386 | 2 |
| #1790 | 29 |