Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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×#19099557 | C2 | semidirect |
| 2. C2×C8×D317 | C2 | semidirect |
| 4. #23778692 | C2 | semidirect |
| 5. #23778692 | C2 | semidirect |
| 6. #23778691 | C2 | semidirect |
| 7. C4⋊C8×C317 | C2 | semidirect |
| 31. #14579261 | D4 | semidirect |
| 43. C2×D317 | M16 | semidirect |
| 55. C317 | #435 | semidirect |
| 60. C4⋊C8 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099557 | 2 |
| C2×C8×D317 | 2 |
| C4×D1268 | 2 |
| #23778692 | 2 |
| #23778691 | 2 |
| C4⋊C8×C317 | 2 |
| #435 | 317 |