Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19104756 | C2 | semidirect |
| 2. C2×#19104754 | C2 | semidirect |
| 3. #23782214 | C2 | semidirect |
| 4. #23782213 | C2 | semidirect |
| 5. #23782060 | C2 | semidirect |
| 6. #23782059 | C2 | semidirect |
| 7. #23782056 | C2 | semidirect |
| 8. #23782053 | C2 | semidirect |
| 9. #23782052 | C2 | semidirect |
| 10. #97×D163 | C2 | semidirect |
| 11. #496×C163 | C2 | semidirect |
| 64. C8×D163 | D4 | semidirect |
| 133. C163 | #3150 | semidirect |
| 144. #496 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| C2×#19104754 | 2 |
| #23782214 | 2 |
| #23782213 | 2 |
| #23782060 | 2 |
| #23782059 | 2 |
| #23782056 | 2 |
| #23782053 | 2 |
| #23782052 | 2 |
| #97×D163 | 2 |
| #496×C163 | 2 |
| #3150 | 163 |