Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104754 | C2 | semidirect |
| 2. #23782319 | C2 | semidirect |
| 3. #23782045 | C2 | semidirect |
| 4. #23781907 | C2 | semidirect |
| 5. #23781870 | C2 | semidirect |
| 6. #23781828 | C2 | semidirect |
| 7. C8×D652 | C2 | semidirect |
| 8. C4×D8×C163 | C2 | semidirect |
| 49. D8×C163 | D4 | semidirect |
| 85. C4×C163 | #135 | semidirect |
| 95. C163 | #3283 | semidirect |
| 103. C4×D8 | D163 | semidirect |
| 137. D8 | D652 | semidirect |
| 183. C4 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| #23782319 | 2 |
| #23782045 | 2 |
| #23781907 | 2 |
| #23781870 | 2 |
| #23781828 | 2 |
| C8×D652 | 2 |
| C4×D8×C163 | 2 |
| #3283 | 163 |