Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 15. #22627558 | C4 | semidirect |
| 16. #22627557 | C4 | semidirect |
| 17. #107×C293 | C4 | semidirect |
| 53. #14556873 | C4⋊C4 | semidirect |
| 56. C8×C293 | C4⋊C4 | semidirect |
| 75. C293 | #1943 | semidirect |
| 90. #107 | #11924078 | semidirect |
| 132. C8 | C4⋊#11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627692 | 2 |
| C2×#22627678 | 2 |
| #34037080 | 2 |
| #34037002 | 2 |
| #107×D293 | 2 |
| #1943 | 293 |