Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104757 | C2 | semidirect |
| 2. #23782215 | C2 | semidirect |
| 3. #23782049 | C2 | semidirect |
| 4. #23782045 | C2 | semidirect |
| 5. #23782042 | C2 | semidirect |
| 6. #23782038 | C2 | semidirect |
| 7. C2×C4×C8×C163 | C2 | semidirect |
| 36. C2×C8×C163 | D4 | semidirect |
| 65. C4×C163 | #135 | semidirect |
| 72. C163 | #3147 | semidirect |
| 80. C2×C4×C8 | D163 | semidirect |
| 107. C2×C8 | D652 | semidirect |
| 139. C4 | #19104757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| #23782215 | 2 |
| #23782049 | 2 |
| #23782045 | 2 |
| #23782042 | 2 |
| #23782038 | 2 |
| C2×C4×C8×C163 | 2 |
| #3147 | 163 |