Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19104659 | C2 | semidirect |
| 3. C2×#19104657 | C2 | semidirect |
| 4. C2×#19104655 | C2 | semidirect |
| 5. C2×(C2×D163)⋊C8 | C2 | semidirect |
| 6. #23781522 | C2 | semidirect |
| 7. C2×#103×C163 | C2 | semidirect |
| 13. C2×#14579700 | C4 | semidirect |
| 94. D652 | C22⋊C4 | semidirect |
| 111. Q8×C163 | C22⋊C4 | semidirect |
| 163. C163 | #1788 | semidirect |
| 167. C2×#103 | D163 | semidirect |
| 258. Q8 | (C2×D163)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579700 | 2 |
| C2×#19104659 | 2 |
| C2×#19104657 | 2 |
| C2×#19104655 | 2 |
| C2×(C2×D163)⋊C8 | 2 |
| #23781522 | 2 |
| C2×#103×C163 | 2 |
| #1788 | 163 |