Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19104675 | C2 | semidirect |
| 3. (C2×D163)⋊C16 | C2 | semidirect |
| 4. C22×C16×C163 | C2 | semidirect |
| 63. C163 | #2113 | semidirect |
| 67. C22×C16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104741 | 2 |
| C2×#19104675 | 2 |
| (C2×D163)⋊C16 | 2 |
| C22×C16×C163 | 2 |
| #2113 | 163 |