Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D541 | C2 | semidirect |
| 3. #31772627 | C2 | semidirect |
| 4. #31772614 | C2 | semidirect |
| 5. #31772613 | C2 | semidirect |
| 6. #31772610 | C2 | semidirect |
| 7. #31772608 | C2 | semidirect |
| 8. #31772607 | C2 | semidirect |
| 9. #31772604 | C2 | semidirect |
| 10. #31772586 | C2 | semidirect |
| 11. C22⋊Q8×C541 | C2 | semidirect |
| 83. C541 | #536 | semidirect |
| 94. C22⋊Q8 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575836 | 2 |
| C2×Q8×D541 | 2 |
| #31772627 | 2 |
| #31772614 | 2 |
| #31772613 | 2 |
| #31772610 | 2 |
| #31772608 | 2 |
| #31772607 | 2 |
| #31772604 | 2 |
| #31772586 | 2 |
| C22⋊Q8×C541 | 2 |
| #536 | 541 |