Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271186 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. C2×#11745185 | C2 | semidirect |
| 5. C2×#11745173 | C2 | semidirect |
| 6. #14271009 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 12. #11745309 | C4 | semidirect |
| 13. #11745306 | C4 | semidirect |
| 14. #11745302 | C4 | semidirect |
| 16. #11745298 | C4 | semidirect |
| 52. C42×C29 | D4 | semidirect |
| 60. C4×Dic29 | D4 | semidirect |
| 125. C2×#104 | D29 | semidirect |
| 152. C29 | #1963 | semidirect |
| 189. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271709 | 2 |
| #14271186 | 2 |
| C2×#11745153 | 2 |
| C2×#11745185 | 2 |
| C2×#11745173 | 2 |
| #14271009 | 2 |
| C2×C29×#104 | 2 |
| #1963 | 29 |