Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#21440151 | C2 | semidirect |
| 2. C2×#21440150 | C2 | semidirect |
| 3. C2×#21440147 | C2 | semidirect |
| 4. #29506378 | C2 | semidirect |
| 5. #29506369 | C2 | semidirect |
| 6. #29506292 | C2 | semidirect |
| 7. C2×D8×C479 | C2 | semidirect |
| 29. C479⋊C8 | D4 | semidirect |
| 37. C8×C479 | D4 | semidirect |
| 54. C479 | #496 | semidirect |
| 59. C2×D8 | D479 | semidirect |
| 92. C8 | C22⋊D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440151 | 2 |
| C2×#21440150 | 2 |
| C2×#21440147 | 2 |
| #29506378 | 2 |
| #29506369 | 2 |
| #29506292 | 2 |
| C2×D8×C479 | 2 |
| #496 | 479 |