Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782377 | C2 | semidirect |
| 2. #23781848 | C2 | semidirect |
| 3. #23781838 | C2 | semidirect |
| 4. #23781463 | C2 | semidirect |
| 5. #23781462 | C2 | semidirect |
| 6. #23781461 | C2 | semidirect |
| 7. #454×C163 | C2 | semidirect |
| 113. C163 | #2204 | semidirect |
| 118. #454 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782377 | 2 |
| #23781848 | 2 |
| #23781838 | 2 |
| #23781463 | 2 |
| #23781462 | 2 |
| #23781461 | 2 |
| #454×C163 | 2 |
| #2204 | 163 |