Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22627645 | C2 | semidirect |
| 2. #34036680 | C2 | semidirect |
| 3. C4×#17989801 | C2 | semidirect |
| 4. #34036354 | C2 | semidirect |
| 5. #34036346 | C2 | semidirect |
| 6. #34036336 | C2 | semidirect |
| 7. #34036330 | C2 | semidirect |
| 8. #34036324 | C2 | semidirect |
| 9. C4⋊C8×D293 | C2 | semidirect |
| 10. #34036124 | C2 | semidirect |
| 11. #461×C293 | C2 | semidirect |
| 47. #17989801 | D4 | semidirect |
| 136. C4×C293 | #135 | semidirect |
| 150. C293 | #3035 | semidirect |
| 158. #461 | D293 | semidirect |
| 292. C4 | #22627645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627645 | 2 |
| #34036680 | 2 |
| C4×#17989801 | 2 |
| #34036354 | 2 |
| #34036346 | 2 |
| #34036336 | 2 |
| #34036330 | 2 |
| #34036324 | 2 |
| C4⋊C8×D293 | 2 |
| #34036124 | 2 |
| #461×C293 | 2 |
| #3035 | 293 |