Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 197 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. #14271542 | C2 | direct (N × H) |
| 41. C2×C4×C29 | Q16 | semidirect |
| 57. C4×C29 | C2×Q16 | semidirect |
| 65. C2×C29 | #494 | semidirect |
| 81. C29 | C2×#494 | semidirect |
| 108. C2×C4 | #90785 | semidirect |
| 120. C4 | C2×#90785 | semidirect |
| 122. C2 | #14271542 | 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×#11745231 | 2 |
| #14271542 | 2 |
| C2×C4×#6597 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| C2×#494 | 29 |