Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104757 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782246 | C2 | semidirect |
| 4. #23781912 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 6. #23781902 | C2 | semidirect |
| 7. #23781664 | C2 | semidirect |
| 8. C2×#107×C163 | C2 | semidirect |
| 55. C2×C8×C163 | D4 | semidirect |
| 108. C163 | #3061 | semidirect |
| 116. C2×#107 | D163 | semidirect |
| 161. C2×C8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| C2×#19104741 | 2 |
| #23782246 | 2 |
| #23781912 | 2 |
| #23781907 | 2 |
| #23781902 | 2 |
| #23781664 | 2 |
| C2×#107×C163 | 2 |
| #3061 | 163 |