Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #31772627 | C2 | semidirect |
| 2. #31772626 | C2 | semidirect |
| 3. #31772623 | C2 | semidirect |
| 4. #31772623 | C2 | semidirect |
| 5. #31772621 | C2 | semidirect |
| 6. #31772621 | C2 | semidirect |
| 7. #31772619 | C2 | semidirect |
| 8. #31772618 | C2 | semidirect |
| 12. #31772607 | C2 | semidirect |
| 13. #31772606 | C2 | semidirect |
| 14. #31772604 | C2 | semidirect |
| 15. C22⋊Q8×C541 | C2 | semidirect |
| 97. C541 | #563 | semidirect |
| 113. C22⋊Q8 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772627 | 2 |
| #31772626 | 2 |
| #31772623 | 2 |
| #31772621 | 2 |
| #31772619 | 2 |
| #31772618 | 2 |
| #31772614 | 2 |
| #31772611 | 2 |
| #31772610 | 2 |
| #31772607 | 2 |
| #31772606 | 2 |
| #31772604 | 2 |
| C22⋊Q8×C541 | 2 |
| #563 | 541 |