Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
| 4. C4×#90779 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 11. Q8×Dic29 | C4 | semidirect |
| 12. Q8×Dic29 | C4 | semidirect |
| 15. D4×Dic29 | C4 | semidirect |
| 16. D4×Dic29 | C4 | semidirect |
| 72. Q8×C29 | C4⋊C4 | semidirect |
| 76. D4×C29 | C4⋊C4 | semidirect |
| 125. Dic29 | #104 | semidirect |
| 160. C29 | #1806 | semidirect |
| 204. Q8 | #90779 | semidirect |
| 208. D4 | #90779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic29 | 2 |
| #14271186 | 2 |
| C2×#11745185 | 2 |
| C4×#90779 | 2 |
| #14270924 | 2 |
| #14270923 | 2 |
| C2×C29×#104 | 2 |
| #1806 | 29 |