Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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. #29506377 | C2 | semidirect |
| 2. #29506373 | C2 | semidirect |
| 3. #29506371 | C2 | semidirect |
| 4. #29506366 | C2 | semidirect |
| 6. Q8×Dic479 | C2 | semidirect |
| 7. #29506344 | C2 | semidirect |
| 8. (C22⋊D479)⋊C4 | C2 | semidirect |
| 9. #29506340 | C2 | semidirect |
| 10. C2×C4×Dic479 | C2 | semidirect |
| 11. C22⋊Q8×C479 | C2 | semidirect |
| 74. C479 | #529 | semidirect |
| 80. C22⋊Q8 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506377 | 2 |
| #29506373 | 2 |
| #29506371 | 2 |
| #29506366 | 2 |
| #29506356 | 2 |
| Q8×Dic479 | 2 |
| #29506344 | 2 |
| (C22⋊D479)⋊C4 | 2 |
| #29506340 | 2 |
| C2×C4×Dic479 | 2 |
| C22⋊Q8×C479 | 2 |
| #529 | 479 |