Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781978 | C2 | semidirect |
| 3. #23781398 | C2 | semidirect |
| 4. #23781389 | C2 | semidirect |
| 5. #397×C163 | C2 | semidirect |
| 13. C22⋊(C163⋊C8) | C22 | semidirect |
| 14. C2×C4⋊C4×C163 | C22 | semidirect |
| 18. #95×C163 | C22 | semidirect |
| 94. C163 | #1607 | semidirect |
| 98. #397 | D163 | semidirect |
| 106. C2×C4⋊C4 | C2×D163 | semidirect |
| 113. #95 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782227 | 2 |
| #23781978 | 2 |
| #23781398 | 2 |
| #23781389 | 2 |
| #397×C163 | 2 |
| #1607 | 163 |