Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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. #14272197 | C2 | semidirect |
| 2. #14272191 | C2 | semidirect |
| 3. #14272027 | C2 | semidirect |
| 4. #14272011 | C2 | semidirect |
| 5. #14272011 | C2 | semidirect |
| 6. #6599⋊C8 | C2 | semidirect |
| 52. D116 | M16 | semidirect |
| 61. #6599 | D8 | semidirect |
| 106. C29 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272197 | 2 |
| #14272191 | 2 |
| #14272027 | 2 |
| #14272011 | 2 |
| #6599⋊C8 | 2 |
| #14271245 | 2 |
| #1581 | 29 |