Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
254 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781978 | C2 | semidirect |
| 3. #23781398 | C2 | semidirect |
| 4. #23781391 | C2 | semidirect |
| 5. #398×C163 | C2 | semidirect |
| 84. C163 | #1610 | semidirect |
| 88. #398 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782246 | 2 |
| #23781978 | 2 |
| #23781398 | 2 |
| #23781391 | 2 |
| #398×C163 | 2 |
| #1610 | 163 |