Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782335 | C2 | semidirect |
| 2. #23782041 | C2 | semidirect |
| 3. #23781866 | C2 | semidirect |
| 4. #23781861 | C2 | semidirect |
| 5. #23781395 | C2 | semidirect |
| 6. #23781392 | C2 | semidirect |
| 7. #331×C163 | C2 | semidirect |
| 55. Dic326 | D8 | semidirect |
| 107. C163 | #1621 | semidirect |
| 113. #331 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782335 | 2 |
| #23782041 | 2 |
| #23781866 | 2 |
| #23781861 | 2 |
| #23781395 | 2 |
| #23781392 | 2 |
| #331×C163 | 2 |
| #1621 | 163 |