Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #34037136 | C2 | semidirect |
| 4. C2×C8×#11924078 | C2 | semidirect |
| 5. #34037005 | C2 | semidirect |
| 6. #34036999 | C2 | semidirect |
| 21. #22627548 | C4 | semidirect |
| 22. #22627546 | C4 | semidirect |
| 23. #22627544 | C4 | semidirect |
| 24. #103×C293 | C4 | semidirect |
| 105. C293 | #1937 | semidirect |
| 125. #103 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037136 | 2 |
| C2×#22627689 | 2 |
| #34037104 | 2 |
| C2×C8×#11924078 | 2 |
| #34037005 | 2 |
| #34036999 | 2 |
| #34036124 | 2 |
| #1937 | 293 |