Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #23781569 | C2 | semidirect |
| 3. #23781562 | C2 | semidirect |
| 6. #23781552 | C2 | semidirect |
| 7. #23781550 | C2 | semidirect |
| 11. #19104714 | C4 | semidirect |
| 110. C163 | #2378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104714 | 2 |
| #23781569 | 2 |
| #23781562 | 2 |
| #23781559 | 2 |
| #23781553 | 2 |
| #23781552 | 2 |
| #23781550 | 2 |
| #23781525 | 2 |
| #381×C163 | 2 |
| #2378 | 163 |