Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. #23781489 | C2 | semidirect |
| 4. #23781488 | C2 | semidirect |
| 5. #23781481 | C2 | semidirect |
| 7. #362×C163 | C2 | semidirect |
| 61. C163 | #2239 | semidirect |
| 68. #362 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781920 | 2 |
| #23781712 | 2 |
| #23781489 | 2 |
| #23781488 | 2 |
| #23781481 | 2 |
| #23781446 | 2 |
| #362×C163 | 2 |
| #2239 | 163 |