Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #34037133 | C2 | semidirect |
| 2. C2×#22627689 | C2 | semidirect |
| 3. C42×#11924078 | C2 | semidirect |
| 11. #22627621 | C4 | semidirect |
| 12. #22627613 | C4 | semidirect |
| 16. C4⋊Q8×C293 | C4 | semidirect |
| 22. C4×#11924078 | D4 | semidirect |
| 63. C4×C293 | #104 | semidirect |
| 72. C293 | #1962 | semidirect |
| 80. C4⋊Q8 | #11924078 | semidirect |
| 139. C4 | #22627689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037133 | 2 |
| C2×#22627689 | 2 |
| C42×#11924078 | 2 |
| #34036680 | 2 |
| #1962 | 293 |