Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
316 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 154 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. #11745220 | C4 | direct (N × H) |
| 28. C4×Dic29 | C8 | semidirect |
| 29. C4×Dic29 | C8 | semidirect |
| 67. C4×C29 | C4⋊C8 | semidirect |
| 69. Dic29 | C4×C8 | semidirect |
| 70. Dic29 | C4⋊C8 | semidirect |
| 94. C29 | C4×C4⋊C8 | semidirect |
| 151. C4 | #11745220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745220 | 2 |
| C2×C4×#6599 | 2 |
| #14272029 | 2 |
| C42×Dic29 | 2 |
| C4×C4⋊C8 | 29 |