Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #31772618 | C2 | semidirect |
| 6. Q8×Dic541 | C2 | semidirect |
| 7. #31772593 | C2 | semidirect |
| 8. #31772593 | C2 | semidirect |
| 38. C2×Dic541 | Q8 | semidirect |
| 70. C541 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772627 | 2 |
| #31772626 | 2 |
| #31772618 | 2 |
| #31772607 | 2 |
| #31772605 | 2 |
| Q8×Dic541 | 2 |
| #31772593 | 2 |
| #31772584 | 2 |
| C2×C4×Dic541 | 2 |
| C22⋊Q8×C541 | 2 |
| #533 | 541 |