Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×#11745229 | C2 | semidirect |
| 2. C2×#11745227 | C2 | semidirect |
| 3. #14272065 | C2 | semidirect |
| 4. #14272063 | C2 | semidirect |
| 6. C22×D4×C29 | C4 | semidirect |
| 10. #11745315 | C4 | semidirect |
| 12. C2×C22⋊Dic29 | C4 | semidirect |
| 17. #11745291 | C4 | semidirect |
| 24. C24×C29 | C2×C4 | semidirect |
| 31. C22×C4×C29 | C2×C4 | semidirect |
| 50. C22⋊Dic29 | C2×C4 | semidirect |
| 51. C22⋊Dic29 | C2×C4 | semidirect |
| 133. C22×D4 | #1181 | semidirect |
| 149. C29 | #2121 | semidirect |
| 152. C24 | C2×#1181 | semidirect |
| 168. C22×C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745229 | 2 |
| C2×#11745227 | 2 |
| #14272065 | 2 |
| #14272063 | 2 |
| #14271722 | 2 |
| #2121 | 29 |