Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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×D479 | C2 | semidirect |
| 3. #29506380 | C2 | semidirect |
| 4. #29506371 | C2 | semidirect |
| 5. #29506370 | C2 | semidirect |
| 6. #29506367 | C2 | semidirect |
| 7. #29506360 | C2 | semidirect |
| 8. #29506339 | C2 | semidirect |
| 9. C4⋊Q8×C479 | C2 | semidirect |
| 63. C479 | #536 | semidirect |
| 68. C4⋊Q8 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440163 | 2 |
| C2×Q8×D479 | 2 |
| #29506380 | 2 |
| #29506371 | 2 |
| #29506370 | 2 |
| #29506367 | 2 |
| #29506360 | 2 |
| #29506339 | 2 |
| C4⋊Q8×C479 | 2 |
| #536 | 479 |