Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#11745304 | C2 | semidirect |
| 3. #14271555 | C2 | semidirect |
| 4. #14271542 | C2 | semidirect |
| 5. #14271537 | C2 | semidirect |
| 6. C4×#90777 | C2 | semidirect |
| 7. C2×C29×C4⋊Q8 | C2 | semidirect |
| 47. #90777 | D4 | semidirect |
| 77. C4×C29 | #137 | semidirect |
| 82. C2×C4⋊Q8 | D29 | semidirect |
| 109. C29 | #3152 | semidirect |
| 161. C4 | #11745304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| #14271713 | 2 |
| #14271555 | 2 |
| #14271542 | 2 |
| #14271537 | 2 |
| C4×#90777 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| #3152 | 29 |