Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 166 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. Q8×#6599 | C2 | semidirect |
| 2. #14272198 | C2 | semidirect |
| 3. #14272180 | C2 | semidirect |
| 4. #14272166 | C2 | semidirect |
| 36. Q8×C29 | M16 | semidirect |
| 84. C29 | #2991 | semidirect |
| 102. Q8 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6599 | 2 |
| #14272198 | 2 |
| #14272180 | 2 |
| #14272166 | 2 |
| #41×Dic29 | 2 |
| #2991 | 29 |