Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
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. #31772623 | C2 | semidirect |
| 2. #31772619 | C2 | semidirect |
| 3. #31772617 | C2 | semidirect |
| 4. #31772612 | C2 | semidirect |
| 6. Q8×Dic541 | C2 | semidirect |
| 7. #31772590 | C2 | semidirect |
| 8. #31772588 | C2 | semidirect |
| 9. #31772586 | C2 | semidirect |
| 10. C2×C4×Dic541 | C2 | semidirect |
| 11. C22⋊Q8×C541 | C2 | semidirect |
| 74. C541 | #529 | semidirect |
| 80. C22⋊Q8 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772623 | 2 |
| #31772619 | 2 |
| #31772617 | 2 |
| #31772612 | 2 |
| #31772602 | 2 |
| Q8×Dic541 | 2 |
| #31772590 | 2 |
| #31772588 | 2 |
| #31772586 | 2 |
| C2×C4×Dic541 | 2 |
| C22⋊Q8×C541 | 2 |
| #529 | 541 |