Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23782073 | C2 | semidirect |
| 4. #23782072 | C2 | semidirect |
| 5. #23782067 | C2 | semidirect |
| 6. #23782064 | C2 | semidirect |
| 7. #23782064 | C2 | semidirect |
| 11. #499×C163 | C2 | semidirect |
| 43. #14579682 | Q8 | semidirect |
| 44. #14579682 | Q8 | semidirect |
| 99. C163 | #3166 | semidirect |
| 108. #499 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782221 | 2 |
| #125×D163 | 2 |
| #23782073 | 2 |
| #23782072 | 2 |
| #23782067 | 2 |
| #23782064 | 2 |
| #23781706 | 2 |
| #23781704 | 2 |
| C4×#14579682 | 2 |
| #499×C163 | 2 |
| #3166 | 163 |