Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22627644 | C2 | semidirect |
| 2. #34036679 | C2 | semidirect |
| 3. #34036524 | C2 | semidirect |
| 4. #34036521 | C2 | semidirect |
| 5. #34036519 | C2 | semidirect |
| 6. #34036516 | C2 | semidirect |
| 7. C2×#22627535 | C2 | semidirect |
| 8. #532×C293 | C2 | semidirect |
| 40. C2×#14556873 | D4 | semidirect |
| 97. C293 | #3150 | semidirect |
| 101. #532 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627644 | 2 |
| #34036679 | 2 |
| #34036524 | 2 |
| #34036521 | 2 |
| #34036519 | 2 |
| #34036516 | 2 |
| C2×#22627535 | 2 |
| #532×C293 | 2 |
| #3150 | 293 |