Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C4×#90785 | C2 | direct (N × H) |
| 17. C2×#90785 | C4 | direct (N × H) |
| 51. #90785 | C2×C4 | direct (N × H) |
| 69. C2×C4×C29 | Q16 | semidirect |
| 94. C4×C29 | C2×Q16 | semidirect |
| 107. C2×C29 | C4×Q16 | semidirect |
| 132. C29 | C2×C4×Q16 | semidirect |
| 179. C2×C4 | #90785 | direct (N × H) |
| 198. C4 | C2×#90785 | direct (N × H) |
| 201. C2 | C4×#90785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C2×C4×Dic58 | 2 |
| C4×#90785 | 2 |
| C2×#11745155 | 2 |
| C2×#11745183 | 2 |
| C2×#11745158 | 2 |
| C2×C4×#6597 | 2 |
| C2×C4×Q8×C29 | 2 |
| C2×C4×Q16 | 29 |