Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×#90777 | C2 | semidirect |
| 3. #14270890 | C2 | semidirect |
| 4. C29×#432 | C2 | semidirect |
| 15. C29×C4⋊C8 | C22 | semidirect |
| 19. C4×#6597 | C22 | semidirect |
| 60. D116 | M16 | semidirect |
| 82. #432 | D29 | semidirect |
| 100. C4⋊C8 | C2×D29 | semidirect |
| 105. C29 | #1490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C4×#90777 | 2 |
| #14270890 | 2 |
| C29×#432 | 2 |
| #1490 | 29 |