Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104758 | C2 | semidirect |
| 2. #23782318 | C2 | semidirect |
| 3. #23781903 | C2 | semidirect |
| 4. #23781867 | C2 | semidirect |
| 5. #23781826 | C2 | semidirect |
| 6. C4×D1304 | C2 | semidirect |
| 7. C8×D652 | C2 | semidirect |
| 8. #494×C163 | C2 | semidirect |
| 38. D1304 | D4 | semidirect |
| 85. C4×C163 | #135 | semidirect |
| 95. C163 | #3283 | semidirect |
| 99. #494 | D163 | semidirect |
| 183. C4 | #19104758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| #23782318 | 2 |
| #23781903 | 2 |
| #23781867 | 2 |
| #23781826 | 2 |
| C4×D1304 | 2 |
| C8×D652 | 2 |
| #494×C163 | 2 |
| #3283 | 163 |