Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 182 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. #14272214 | C2 | semidirect |
| 2. Q8×#6599 | C2 | semidirect |
| 26. #90800 | Q8 | direct (N × H) |
| 38. Q8×C29 | M16 | semidirect |
| 50. #6599 | C2×Q8 | semidirect |
| 85. C29 | Q8×M16 | semidirect |
| 105. Q8 | #90800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| Q8×#6599 | 2 |
| #14272166 | 2 |
| C4×#90800 | 2 |
| C2×Q8×Dic29 | 2 |
| Q8×M16 | 29 |