Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
272 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 17. #11745218 | C4 | semidirect |
| 18. #11745218 | C4 | semidirect |
| 21. C29×C4⋊C8 | C4 | semidirect |
| 22. #11745162 | C4 | semidirect |
| 23. #11745162 | C4 | semidirect |
| 24. C4⋊#6597 | C4 | semidirect |
| 73. #6599 | C4⋊C4 | semidirect |
| 117. C4⋊C8 | #1181 | semidirect |
| 123. C29 | #1771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272122 | 2 |
| C2×#11745208 | 2 |
| C2×C8×#1181 | 2 |
| C4×C4⋊#1181 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C4⋊C8×D29 | 2 |
| #1771 | 29 |