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. #14271525 | C2 | semidirect |
| 4. #14271523 | C2 | semidirect |
| 5. #14271522 | C2 | semidirect |
| 6. #14271512 | C2 | semidirect |
| 7. #14271508 | C2 | semidirect |
| 8. #14271163 | C2 | semidirect |
| 9. #14271161 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#489 | C2 | semidirect |
| 140. #489 | D29 | semidirect |
| 183. C29 | #3141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271712 | 2 |
| C4⋊Q8×D29 | 2 |
| #14271525 | 2 |
| #14271523 | 2 |
| #14271522 | 2 |
| #14271512 | 2 |
| #14271508 | 2 |
| #14271163 | 2 |
| #14271161 | 2 |
| #14271115 | 2 |
| C29×#489 | 2 |
| #3141 | 29 |