Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #34037144 | C2 | semidirect |
| 4. M16×#11924078 | C2 | semidirect |
| 5. #34037012 | C2 | semidirect |
| 6. #34037001 | C2 | semidirect |
| 23. #22627542 | C4 | semidirect |
| 24. #22627542 | C4 | semidirect |
| 25. #22627541 | C4 | semidirect |
| 26. #100×C293 | C4 | semidirect |
| 105. C293 | #1932 | semidirect |
| 130. #100 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037144 | 2 |
| #34037127 | 2 |
| C2×#22627688 | 2 |
| M16×#11924078 | 2 |
| #34037012 | 2 |
| #34037001 | 2 |
| #34036110 | 2 |
| #1932 | 293 |