Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 287 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 |
|---|---|---|
| 13. Q8×Dic29 | C4 | semidirect |
| 39. #90779 | Q8 | direct (N × H) |
| 43. Q8×C29 | C4⋊C4 | semidirect |
| 79. Dic29 | C4×Q8 | semidirect |
| 109. C29 | Q8×C4⋊C4 | semidirect |
| 130. Q8 | #90779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic29 | 2 |
| #14271061 | 2 |
| #14271059 | 2 |
| #14271032 | 2 |
| C4×#90779 | 2 |
| C2×C4×Q8×C29 | 2 |
| Q8×C4⋊C4 | 29 |