Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D29 | C2 | semidirect |
| 3. #14271475 | C2 | semidirect |
| 4. #14271459 | C2 | semidirect |
| 5. #14271458 | C2 | semidirect |
| 6. #14271360 | C2 | semidirect |
| 7. #14271300 | C2 | semidirect |
| 8. #14271264 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#460 | C2 | semidirect |
| 86. Q8×C29 | #41 | semidirect |
| 113. Dic58 | #41 | semidirect |
| 142. #460 | D29 | semidirect |
| 183. C29 | #3112 | semidirect |
| 231. Q8 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271711 | 2 |
| C4×Q8×D29 | 2 |
| #14271475 | 2 |
| #14271459 | 2 |
| #14271458 | 2 |
| #14271360 | 2 |
| #14271300 | 2 |
| #14271264 | 2 |
| #14271260 | 2 |
| #14271219 | 2 |
| C29×#460 | 2 |
| #3112 | 29 |