Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19104669 | C2 | semidirect |
| 3. #23781467 | C2 | direct (N × H) |
| 4. C22×C16×C163 | C2 | semidirect |
| 8. C2×D1304 | C4 | semidirect |
| 12. #19104669 | C22 | semidirect |
| 15. C2×C16×C163 | C22 | semidirect |
| 24. D1304 | C2×C4 | semidirect |
| 62. C2×C163 | #357 | semidirect |
| 67. C163 | C2×#357 | semidirect |
| 70. C22×C16 | D163 | semidirect |
| 81. C2×C16 | C2×D163 | semidirect |
| 131. C2 | #23781467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| C2×#19104669 | 2 |
| #23781467 | 2 |
| C22×C16×C163 | 2 |
| C2×#357 | 163 |