Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782220 | C2 | semidirect |
| 3. #23782038 | C2 | semidirect |
| 4. #23782017 | C2 | semidirect |
| 5. #23782013 | C2 | semidirect |
| 6. #23781895 | C2 | semidirect |
| 7. #23781752 | C2 | semidirect |
| 8. C4×C8×D163 | C2 | semidirect |
| 9. #498×C163 | C2 | semidirect |
| 81. C4×D163 | SD16 | semidirect |
| 90. C8×C163 | #41 | semidirect |
| 112. C163 | #3167 | semidirect |
| 116. #498 | D163 | semidirect |
| 203. C8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| #23782216 | 2 |
| #23782038 | 2 |
| #23782017 | 2 |
| #23782013 | 2 |
| #23781895 | 2 |
| #23781752 | 2 |
| C4×C8×D163 | 2 |
| #498×C163 | 2 |
| #3167 | 163 |