Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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×#19104678 | C2 | semidirect |
| 2. C2×#19104675 | C2 | semidirect |
| 4. #23781490 | C2 | semidirect |
| 5. #23781469 | C2 | semidirect |
| 6. #23781465 | C2 | semidirect |
| 7. #467×C163 | C2 | semidirect |
| 28. C163⋊C16 | D4 | semidirect |
| 75. C163 | #2220 | semidirect |
| 79. #467 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104678 | 2 |
| C2×#19104675 | 2 |
| #23781901 | 2 |
| #23781490 | 2 |
| #23781469 | 2 |
| #23781465 | 2 |
| #467×C163 | 2 |
| #2220 | 163 |