Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271878 | C2 | semidirect |
| 2. #14271513 | C2 | semidirect |
| 3. #14271501 | C2 | semidirect |
| 4. #14271453 | C2 | semidirect |
| 5. #14271394 | C2 | semidirect |
| 6. #14271365 | C2 | semidirect |
| 7. #14271308 | C2 | semidirect |
| 8. C4×#90782 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. #14271159 | C2 | semidirect |
| 11. C29×#547 | C2 | semidirect |
| 126. #547 | D29 | semidirect |
| 171. C29 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271878 | 2 |
| #14271513 | 2 |
| #14271501 | 2 |
| #14271453 | 2 |
| #14271394 | 2 |
| #14271365 | 2 |
| #14271308 | 2 |
| C4×#90782 | 2 |
| D4×#6597 | 2 |
| #14271159 | 2 |
| C29×#547 | 2 |
| #3303 | 29 |