Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #32914597 | C2 | semidirect |
| 4. #32914588 | C2 | semidirect |
| 6. #32914575 | C2 | semidirect |
| 7. C4×Q8×C577 | C2 | semidirect |
| 10. #22604405 | C4 | semidirect |
| 26. #17987230 | C2×C4 | semidirect |
| 28. Q8×C577 | C2×C4 | semidirect |
| 49. C577 | #440 | semidirect |
| 52. C4×Q8 | D577 | semidirect |
| 72. Q8 | C4×D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22604405 | 2 |
| C4×D2308 | 2 |
| #32914597 | 2 |
| #32914588 | 2 |
| #32914584 | 2 |
| #32914575 | 2 |
| C4×Q8×C577 | 2 |
| #440 | 577 |