Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #23782139 | C2 | semidirect |
| 3. #23781683 | C2 | semidirect |
| 4. #23781669 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #23781436 | C2 | semidirect |
| 7. H(3,ℤ/4)×C163 | C2 | semidirect |
| 12. C2×#14579688 | C4 | semidirect |
| 13. C2×D1304 | C4 | semidirect |
| 30. C2×Dic326 | C2×C4 | semidirect |
| 35. C2×D652 | C2×C4 | semidirect |
| 53. C2×C8×C163 | C2×C4 | semidirect |
| 115. C163 | #1904 | semidirect |
| 123. H(3,ℤ/4) | D163 | semidirect |
| 165. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| #23782139 | 2 |
| #23781683 | 2 |
| #23781669 | 2 |
| #23781638 | 2 |
| #23781436 | 2 |
| H(3,ℤ/4)×C163 | 2 |
| #1904 | 163 |