Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782213 | C2 | semidirect |
| 3. #23782048 | C2 | semidirect |
| 4. #23782045 | C2 | semidirect |
| 5. #23782037 | C2 | semidirect |
| 6. C4×C8×D163 | C2 | semidirect |
| 7. #493×C163 | C2 | semidirect |
| 32. C8×D163 | D4 | semidirect |
| 63. C4×C163 | #135 | semidirect |
| 72. C163 | #3147 | semidirect |
| 78. #493 | D163 | semidirect |
| 139. 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 |
| #23782213 | 2 |
| #23782048 | 2 |
| #23782045 | 2 |
| #23782037 | 2 |
| C4×C8×D163 | 2 |
| #493×C163 | 2 |
| #3147 | 163 |