Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14271718 | C2 | semidirect |
| 3. #14271469 | C2 | semidirect |
| 4. #14271461 | C2 | semidirect |
| 5. #14271459 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 7. #14271445 | C2 | semidirect |
| 8. #14271200 | C2 | semidirect |
| 9. C4⋊C8×D29 | C2 | semidirect |
| 11. C29×#474 | C2 | semidirect |
| 50. #90807 | Q8 | semidirect |
| 137. #474 | D29 | semidirect |
| 177. C29 | #3076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×#90807 | 2 |
| #14271469 | 2 |
| #14271461 | 2 |
| #14271459 | 2 |
| #14271453 | 2 |
| #14271445 | 2 |
| #14271200 | 2 |
| C4⋊C8×D29 | 2 |
| #14271156 | 2 |
| C29×#474 | 2 |
| #3076 | 29 |