Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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. #14272113 | C2 | semidirect |
| 2. #14272105 | C2 | semidirect |
| 4. C4×C22⋊#1181 | C2 | semidirect |
| 12. C2×C4⋊#1181 | C22 | semidirect |
| 13. C2×C4×#1181 | C22 | semidirect |
| 14. C2×C22⋊C4×C29 | C4 | semidirect |
| 15. C2×C22⋊Dic29 | C4 | semidirect |
| 16. C2×#90781 | C4 | semidirect |
| 17. C2×#90781 | C4 | semidirect |
| 18. C22⋊C4×D29 | C4 | semidirect |
| 20. (C2×#1181)⋊C4 | C22 | semidirect |
| 21. (C2×#1181)⋊C4 | C22 | semidirect |
| 138. C2×C22⋊C4 | #1181 | semidirect |
| 142. C29 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272113 | 2 |
| #14272105 | 2 |
| #14272104 | 2 |
| C4×C22⋊#1181 | 2 |
| C2×C22⋊C4×D29 | 2 |
| #2312 | 29 |