Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#19099561 | C2 | semidirect |
| 2. C22×#14579261 | C2 | semidirect |
| 4. #23778711 | C2 | semidirect |
| 5. #23778704 | C2 | semidirect |
| 6. #23778700 | C2 | semidirect |
| 7. C22⋊Q8×C317 | C2 | semidirect |
| 27. #14579261 | D4 | semidirect |
| 39. C22×C317 | SD16 | semidirect |
| 55. C317 | #465 | semidirect |
| 59. C22⋊Q8 | D317 | semidirect |
| 98. C22 | #19099561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099561 | 2 |
| C22×#14579261 | 2 |
| #23778754 | 2 |
| #23778711 | 2 |
| #23778704 | 2 |
| #23778700 | 2 |
| C22⋊Q8×C317 | 2 |
| #465 | 317 |