Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782270 | C2 | semidirect |
| 2. #23782067 | C2 | semidirect |
| 3. #23782042 | C2 | semidirect |
| 4. #23782030 | C2 | semidirect |
| 5. #23781918 | C2 | semidirect |
| 6. #23781901 | C2 | semidirect |
| 7. #23781778 | C2 | semidirect |
| 8. C4×D1304 | C2 | semidirect |
| 9. #405×C163 | C2 | semidirect |
| 84. C163 | #3176 | semidirect |
| 94. #405 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23782067 | 2 |
| #23782042 | 2 |
| #23782030 | 2 |
| #23781918 | 2 |
| #23781901 | 2 |
| #23781778 | 2 |
| C4×D1304 | 2 |
| #405×C163 | 2 |
| #3176 | 163 |