Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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. #34037134 | C2 | semidirect |
| 2. C2×#22627689 | C2 | semidirect |
| 3. #34037065 | C2 | semidirect |
| 11. #22627621 | C4 | semidirect |
| 12. #22627613 | C4 | semidirect |
| 16. C4⋊Q8×C293 | C4 | semidirect |
| 21. C4×#11924078 | D4 | semidirect |
| 71. C293 | #1963 | semidirect |
| 79. C4⋊Q8 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037134 | 2 |
| C2×#22627689 | 2 |
| #34037065 | 2 |
| #34036680 | 2 |
| #1963 | 293 |