Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23781565 | C2 | semidirect |
| 3. #23781557 | C2 | semidirect |
| 4. #23781548 | C2 | semidirect |
| 5. #23781543 | C2 | semidirect |
| 6. #23781541 | C2 | semidirect |
| 7. #23781539 | C2 | semidirect |
| 8. #23781525 | C2 | semidirect |
| 9. #381×C163 | C2 | semidirect |
| 13. #19104709 | C4 | semidirect |
| 37. C2×C22⋊D163 | C2×C4 | semidirect |
| 45. C4⋊Dic163 | C2×C4 | semidirect |
| 52. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 56. C22×C4×C163 | C2×C4 | semidirect |
| 129. C163 | #2377 | semidirect |
| 138. #381 | D163 | semidirect |
| 176. C22×C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104709 | 2 |
| #23781565 | 2 |
| #23781557 | 2 |
| #23781548 | 2 |
| #23781543 | 2 |
| #23781541 | 2 |
| #23781539 | 2 |
| #23781525 | 2 |
| #381×C163 | 2 |
| #2377 | 163 |