Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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. #14271267 | C2 | direct (N × H) |
| 15. C2×#90785 | C4 | semidirect |
| 49. #90785 | C2×C4 | semidirect |
| 107. C2×C29 | #441 | semidirect |
| 132. C29 | C2×#441 | semidirect |
| 201. C2 | #14271267 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C2×Q8×Dic29 | 2 |
| C2×#11745249 | 2 |
| #14271267 | 2 |
| C2×#11745156 | 2 |
| C2×#11745164 | 2 |
| C2×#11745163 | 2 |
| C2×C29×#103 | 2 |
| C2×#441 | 29 |