Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #29506381 | C2 | semidirect |
| 2. #29506380 | C2 | semidirect |
| 3. #29506377 | C2 | semidirect |
| 4. #29506377 | C2 | semidirect |
| 5. #29506375 | C2 | semidirect |
| 6. #29506375 | C2 | semidirect |
| 7. #29506373 | C2 | semidirect |
| 8. #29506372 | C2 | semidirect |
| 12. #29506361 | C2 | semidirect |
| 13. #29506360 | C2 | semidirect |
| 14. #29506358 | C2 | semidirect |
| 15. C22⋊Q8×C479 | C2 | semidirect |
| 97. C479 | #563 | semidirect |
| 113. C22⋊Q8 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506381 | 2 |
| #29506380 | 2 |
| #29506377 | 2 |
| #29506375 | 2 |
| #29506373 | 2 |
| #29506372 | 2 |
| #29506368 | 2 |
| #29506365 | 2 |
| #29506364 | 2 |
| #29506361 | 2 |
| #29506360 | 2 |
| #29506358 | 2 |
| C22⋊Q8×C479 | 2 |
| #563 | 479 |