Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D1172 | C2 | semidirect |
| 2. #34036488 | C2 | semidirect |
| 3. #34036479 | C2 | semidirect |
| 4. #34036424 | C2 | semidirect |
| 5. #34036409 | C2 | semidirect |
| 7. #34036331 | C2 | semidirect |
| 8. #34036260 | C2 | semidirect |
| 9. #34036227 | C2 | semidirect |
| 11. #556×C293 | C2 | semidirect |
| 122. C293 | #3367 | semidirect |
| 124. #556 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1172 | 2 |
| #34036488 | 2 |
| #34036479 | 2 |
| #34036424 | 2 |
| #34036409 | 2 |
| #34036341 | 2 |
| #34036331 | 2 |
| #34036260 | 2 |
| #34036227 | 2 |
| C4×#17989787 | 2 |
| #556×C293 | 2 |
| #3367 | 293 |