Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 55. #6599 | Q16 | semidirect |
| 94. C29 | #1584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272213 | 2 |
| #14272212 | 2 |
| #14272027 | 2 |
| #14272013 | 2 |
| #6599⋊C8 | 2 |
| #14271257 | 2 |
| #1584 | 29 |