Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
310 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #23781798 | C2 | semidirect |
| 2. #23781582 | C2 | semidirect |
| 3. #23781399 | C2 | semidirect |
| 4. #23781391 | C2 | semidirect |
| 5. #537×C163 | C2 | semidirect |
| 71. C2×C4×C163 | D8 | semidirect |
| 100. C163 | #1598 | semidirect |
| 102. #537 | D163 | semidirect |
| 171. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781798 | 2 |
| #23781582 | 2 |
| #23781399 | 2 |
| #23781391 | 2 |
| #537×C163 | 2 |
| #1598 | 163 |