Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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×D2608 | C2 | semidirect |
| 2. #23781901 | C2 | semidirect |
| 3. #23781491 | C2 | semidirect |
| 4. #23781467 | C2 | semidirect |
| 5. C22×C16×C163 | C2 | semidirect |
| 27. C16×C163 | D4 | semidirect |
| 43. C22×C163 | D16 | semidirect |
| 57. C163 | #2215 | semidirect |
| 60. C22×C16 | D163 | semidirect |
| 85. C16 | C22⋊D163 | semidirect |
| 104. C22 | D2608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2608 | 2 |
| #23781901 | 2 |
| #23781491 | 2 |
| #23781467 | 2 |
| C22×C16×C163 | 2 |
| #2215 | 163 |