Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #14271030 | C2 | semidirect |
| 3. #14271027 | C2 | semidirect |
| 6. C4×#90779 | C2 | semidirect |
| 8. #14271009 | C2 | semidirect |
| 9. C29×#376 | C2 | semidirect |
| 21. C42×D29 | C4 | semidirect |
| 102. #376 | D29 | semidirect |
| 126. C29 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D29 | 2 |
| #14271030 | 2 |
| #14271027 | 2 |
| #14271025 | 2 |
| #14271022 | 2 |
| C4×#90779 | 2 |
| C4×#90781 | 2 |
| #14271009 | 2 |
| C29×#376 | 2 |
| #2283 | 29 |