Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
166 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 58 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. #14272213 | C2 | semidirect |
| 3. #14272024 | C2 | semidirect |
| 4. #14272013 | C2 | semidirect |
| 6. C8×#6599 | C2 | semidirect |
| 58. #6599 | SD16 | semidirect |
| 59. C8×C29 | M16 | semidirect |
| 100. C29 | #1590 | semidirect |
| 138. C8 | #90796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272213 | 2 |
| #14272197 | 2 |
| #14272024 | 2 |
| #14272013 | 2 |
| #14272011 | 2 |
| C8×#6599 | 2 |
| #14271250 | 2 |
| #1590 | 29 |