Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#11745155 | C2 | semidirect |
| 4. #14271061 | C2 | semidirect |
| 5. #14270925 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 21. #11745180 | C4 | semidirect |
| 48. C4⋊Dic29 | C2×C4 | semidirect |
| 55. C2×#6597 | C2×C4 | semidirect |
| 67. D4×C29 | C4⋊C4 | semidirect |
| 147. C29 | #1862 | semidirect |
| 191. D4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745155 | 2 |
| C2×#11745180 | 2 |
| #14271061 | 2 |
| #14270925 | 2 |
| #14270918 | 2 |
| C2×C4×D4×C29 | 2 |
| #1862 | 29 |