Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271559 | C2 | semidirect |
| 2. #14271448 | C2 | semidirect |
| 4. #14270909 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 55. Q8×C29 | SD16 | semidirect |
| 117. C29 | #1651 | semidirect |
| 150. Q8 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271559 | 2 |
| #14271448 | 2 |
| #14271368 | 2 |
| #14270909 | 2 |
| Q8⋊#6597 | 2 |
| D4⋊#6597 | 2 |
| D4×Q8×C29 | 2 |
| #1651 | 29 |