Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 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 |
|---|---|---|
| 1. #23782100 | C2 | semidirect |
| 2. C2×#19104678 | C2 | semidirect |
| 3. #23781935 | C2 | semidirect |
| 4. #23781481 | C2 | semidirect |
| 5. #23781472 | C2 | semidirect |
| 6. #23781449 | C2 | semidirect |
| 7. #578×C163 | C2 | semidirect |
| 90. C163 | #2193 | semidirect |
| 92. #578 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782100 | 2 |
| C2×#19104678 | 2 |
| #23781935 | 2 |
| #23781481 | 2 |
| #23781472 | 2 |
| #23781449 | 2 |
| #578×C163 | 2 |
| #2193 | 163 |