Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #23781604 | C2 | semidirect |
| 3. #23781591 | C2 | semidirect |
| 5. #23781576 | C2 | semidirect |
| 6. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 7. #23781511 | C2 | semidirect |
| 8. C2×C4×Q8×C163 | C2 | semidirect |
| 96. C163 | #2398 | semidirect |
| 98. C2×C4×Q8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D652 | 2 |
| #23781604 | 2 |
| #23781591 | 2 |
| #23781582 | 2 |
| #23781576 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| #23781511 | 2 |
| C2×C4×Q8×C163 | 2 |
| #2398 | 163 |