Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #14271514 | C2 | semidirect |
| 4. #14271499 | C2 | semidirect |
| 5. #14271459 | C2 | semidirect |
| 6. #14271404 | C2 | semidirect |
| 7. #14271374 | C2 | semidirect |
| 8. #14271321 | C2 | semidirect |
| 9. C4×Dic116 | C2 | semidirect |
| 10. C2×#11745164 | C2 | semidirect |
| 77. D4×C29 | Q16 | semidirect |
| 163. C29 | #3299 | semidirect |
| 208. D4 | Dic116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| D4×Dic58 | 2 |
| #14271514 | 2 |
| #14271499 | 2 |
| #14271459 | 2 |
| #14271404 | 2 |
| #14271374 | 2 |
| #14271321 | 2 |
| C4×Dic116 | 2 |
| C2×#11745164 | 2 |
| C8×D4×C29 | 2 |
| #3299 | 29 |