Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #34037078 | C2 | semidirect |
| 3. C4×C4⋊#11924078 | C2 | semidirect |
| 5. #34037065 | C2 | semidirect |
| 6. C42×#11924078 | C2 | semidirect |
| 17. #22627583 | C4 | semidirect |
| 18. #22627582 | C4 | semidirect |
| 19. #22627581 | C4 | semidirect |
| 20. #22627581 | C4 | semidirect |
| 21. #22627580 | C4 | semidirect |
| 26. #117×C293 | C4 | semidirect |
| 108. C293 | #2298 | semidirect |
| 123. #117 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037079 | 2 |
| #34037078 | 2 |
| C4×C4⋊#11924078 | 2 |
| C4×C22⋊#11924078 | 2 |
| #34037065 | 2 |
| C42×#11924078 | 2 |
| #117×D293 | 2 |
| #2298 | 293 |