Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #32914659 | C2 | semidirect |
| 2. #32914655 | C2 | semidirect |
| 3. #32914653 | C2 | semidirect |
| 4. #32914648 | C2 | semidirect |
| 6. Q8×Dic577 | C2 | semidirect |
| 7. #32914626 | C2 | semidirect |
| 8. #32914624 | C2 | semidirect |
| 9. #32914622 | C2 | semidirect |
| 10. C2×C4×Dic577 | C2 | semidirect |
| 11. C22⋊Q8×C577 | C2 | semidirect |
| 74. C577 | #529 | semidirect |
| 80. C22⋊Q8 | D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32914659 | 2 |
| #32914655 | 2 |
| #32914653 | 2 |
| #32914648 | 2 |
| #32914638 | 2 |
| Q8×Dic577 | 2 |
| #32914626 | 2 |
| #32914624 | 2 |
| #32914622 | 2 |
| C2×C4×Dic577 | 2 |
| C22⋊Q8×C577 | 2 |
| #529 | 577 |