Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #14272134 | C2 | semidirect |
| 2. C2×(C2×#1181)⋊C4 | C2 | semidirect |
| 3. #14272017 | C2 | semidirect |
| 4. #14272015 | C2 | semidirect |
| 7. C2×#90809 | C4 | semidirect |
| 10. C29×C22⋊Q8 | C4 | semidirect |
| 12. #11745292 | C4 | semidirect |
| 16. #11745254 | C4 | semidirect |
| 28. C2×Q8×C29 | C2×C4 | semidirect |
| 35. C2×D116 | C2×C4 | semidirect |
| 45. C4⋊C4×C29 | C2×C4 | semidirect |
| 51. C4⋊Dic29 | C2×C4 | semidirect |
| 131. C22⋊Q8 | #1181 | semidirect |
| 142. C29 | #1504 | semidirect |
| 145. C2×Q8 | C2×#1181 | semidirect |
| 167. C4⋊C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272134 | 2 |
| C2×(C2×#1181)⋊C4 | 2 |
| #14272017 | 2 |
| #14272015 | 2 |
| #14271676 | 2 |
| #1504 | 29 |