Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #29506407 | C2 | semidirect |
| 2. C2×#21440147 | C2 | semidirect |
| 3. #29506389 | C2 | semidirect |
| 4. #29506317 | C2 | semidirect |
| 5. #29506299 | C2 | semidirect |
| 6. #29506298 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C479 | C2 | semidirect |
| 53. C479 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506407 | 2 |
| C2×#21440147 | 2 |
| #29506389 | 2 |
| #29506317 | 2 |
| #29506299 | 2 |
| #29506298 | 2 |
| AGL(1,ℤ/8)×C479 | 2 |
| #472 | 479 |