Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23781701 | C2 | semidirect |
| 3. #23781683 | C2 | semidirect |
| 4. #23781682 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781621 | C2 | semidirect |
| 7. #410×C163 | C2 | semidirect |
| 13. C2×#14579689 | C4 | semidirect |
| 14. C2×#14579687 | C4 | semidirect |
| 15. C2×#14579686 | C4 | semidirect |
| 16. C2×#14579684 | C4 | semidirect |
| 132. C163 | #1976 | semidirect |
| 139. #410 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| #23781701 | 2 |
| #23781683 | 2 |
| #23781682 | 2 |
| #23781638 | 2 |
| #23781621 | 2 |
| #410×C163 | 2 |
| #1976 | 163 |