Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. Q8×D116 | C2 | semidirect |
| 2. #14271522 | C2 | semidirect |
| 3. #14271513 | C2 | semidirect |
| 4. #14271458 | C2 | semidirect |
| 5. #14271443 | C2 | semidirect |
| 7. #14271365 | C2 | semidirect |
| 8. #14271294 | C2 | semidirect |
| 9. #14271261 | C2 | semidirect |
| 11. C29×#556 | C2 | semidirect |
| 118. #556 | D29 | semidirect |
| 163. C29 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D116 | 2 |
| #14271522 | 2 |
| #14271513 | 2 |
| #14271458 | 2 |
| #14271443 | 2 |
| #14271375 | 2 |
| #14271365 | 2 |
| #14271294 | 2 |
| #14271261 | 2 |
| C4×#90782 | 2 |
| C29×#556 | 2 |
| #3367 | 29 |