Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 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 |
|---|---|---|
| 7. C4×Q8×C29 | C4 | semidirect |
| 10. Q8×Dic29 | C4 | direct (N × H) |
| 30. C4×Dic29 | Q8 | direct (N × H) |
| 32. Q8×C29 | C42 | semidirect |
| 54. C4×C29 | C4×Q8 | semidirect |
| 56. Dic29 | C4×Q8 | direct (N × H) |
| 69. C4×Q8 | Dic29 | direct (N × H) |
| 78. C29 | C42×Q8 | semidirect |
| 94. Q8 | C4×Dic29 | direct (N × H) |
| 117. C4 | Q8×Dic29 | 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 |
| C4⋊C4×Dic29 | 2 |
| C4×C4⋊Dic29 | 2 |
| C42×Dic29 | 2 |
| C2×C4×Q8×C29 | 2 |
| C42×Q8 | 29 |