Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic29 | C2 | semidirect |
| 3. #14271477 | C2 | semidirect |
| 4. #14271474 | C2 | semidirect |
| 5. #14271456 | C2 | semidirect |
| 6. #14271361 | C2 | semidirect |
| 7. #14271302 | C2 | semidirect |
| 8. #14271266 | C2 | semidirect |
| 9. #14271264 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 11. C29×#448 | C2 | semidirect |
| 87. Q8×C29 | #41 | semidirect |
| 142. #448 | D29 | semidirect |
| 183. C29 | #3112 | semidirect |
| 229. Q8 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271708 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271477 | 2 |
| #14271474 | 2 |
| #14271456 | 2 |
| #14271361 | 2 |
| #14271302 | 2 |
| #14271266 | 2 |
| #14271264 | 2 |
| #14271217 | 2 |
| C29×#448 | 2 |
| #3112 | 29 |