Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782202 | C2 | semidirect |
| 2. #23782066 | C2 | semidirect |
| 3. #23782050 | C2 | semidirect |
| 4. #23782021 | C2 | semidirect |
| 5. #23781903 | C2 | semidirect |
| 7. #23781897 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. C4×D1304 | C2 | semidirect |
| 10. C4×C8×D163 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 118. C163 | #3168 | semidirect |
| 127. C4×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782202 | 2 |
| #23782066 | 2 |
| #23782050 | 2 |
| #23782021 | 2 |
| #23781903 | 2 |
| #23781902 | 2 |
| #23781897 | 2 |
| C4×#14579686 | 2 |
| C4×D1304 | 2 |
| C4×C8×D163 | 2 |
| C4×Q16×C163 | 2 |
| #3168 | 163 |