Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #14271476 | C2 | semidirect |
| 3. #14271458 | C2 | semidirect |
| 4. #14271363 | C2 | semidirect |
| 5. #14271302 | C2 | semidirect |
| 6. #14271261 | C2 | semidirect |
| 7. #14271220 | C2 | semidirect |
| 8. C2×C4×Q8×C29 | C2 | semidirect |
| 68. Q8×C29 | #41 | semidirect |
| 108. C2×C4×Q8 | D29 | semidirect |
| 144. C29 | #3112 | semidirect |
| 181. Q8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271476 | 2 |
| #14271458 | 2 |
| #14271363 | 2 |
| #14271302 | 2 |
| #14271261 | 2 |
| #14271220 | 2 |
| C2×C4×Q8×C29 | 2 |
| #3112 | 29 |