Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
684 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 381 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 |
|---|---|---|
| 14. C4×Dic58 | C4 | direct (N × H) |
| 24. C42×C29 | Q8 | semidirect |
| 39. Dic58 | C42 | direct (N × H) |
| 46. C4×C29 | C4×Q8 | semidirect |
| 67. C29 | C42×Q8 | semidirect |
| 79. C42 | Dic58 | direct (N × H) |
| 98. C4 | C4×Dic58 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic58 | 2 |
| C4×#90779 | 2 |
| C4×C4⋊Dic29 | 2 |
| C42×Dic29 | 2 |
| C43×C29 | 2 |
| C42×Q8 | 29 |