Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782013 | C2 | semidirect |
| 3. #23781872 | C2 | semidirect |
| 4. #23781408 | C2 | semidirect |
| 5. #23781395 | C2 | semidirect |
| 6. D4⋊(C163⋊C8) | C2 | semidirect |
| 7. #474×C163 | C2 | semidirect |
| 99. C163 | #1641 | semidirect |
| 103. #474 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782336 | 2 |
| #23782013 | 2 |
| #23781872 | 2 |
| #23781408 | 2 |
| #23781395 | 2 |
| D4⋊(C163⋊C8) | 2 |
| #474×C163 | 2 |
| #1641 | 163 |