Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
258 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23781854 | C2 | semidirect |
| 3. #23781842 | C2 | semidirect |
| 4. #23781460 | C2 | semidirect |
| 5. #23781455 | C2 | semidirect |
| 6. #23781452 | C2 | semidirect |
| 7. #551×C163 | C2 | semidirect |
| 42. C2×Q8×C163 | D4 | semidirect |
| 47. C22×C4×C163 | D4 | semidirect |
| 59. C22⋊C4×C163 | D4 | semidirect |
| 61. C42×C163 | D4 | semidirect |
| 121. C163 | #2197 | semidirect |
| 123. #551 | D163 | semidirect |
| 152. C2×Q8 | C22⋊D163 | semidirect |
| 161. C22×C4 | C22⋊D163 | semidirect |
| 181. C22⋊C4 | C22⋊D163 | semidirect |
| 183. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781854 | 2 |
| #23781851 | 2 |
| #23781842 | 2 |
| #23781460 | 2 |
| #23781455 | 2 |
| #23781452 | 2 |
| #551×C163 | 2 |
| #2197 | 163 |