Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #29506372 | C2 | semidirect |
| 5. #29506362 | C2 | semidirect |
| 6. #29506361 | C2 | semidirect |
| 7. #29506347 | C2 | semidirect |
| 9. #29506341 | C2 | semidirect |
| 10. #29506340 | C2 | semidirect |
| 11. C2×C4⋊C4×C479 | C2 | semidirect |
| 72. C479 | #552 | semidirect |
| 84. C2×C4⋊C4 | 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 |
| #29506372 | 2 |
| #29506365 | 2 |
| #29506362 | 2 |
| #29506361 | 2 |
| #29506347 | 2 |
| C4×C22⋊D479 | 2 |
| #29506341 | 2 |
| #29506340 | 2 |
| C2×C4⋊C4×C479 | 2 |
| #552 | 479 |