Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782330 | C2 | semidirect |
| 3. #23782015 | C2 | semidirect |
| 4. #23781994 | C2 | semidirect |
| 5. #23781951 | C2 | semidirect |
| 6. #23781891 | C2 | semidirect |
| 7. #23781802 | C2 | semidirect |
| 8. C4×#14579687 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #103×D163 | C2 | semidirect |
| 11. #461×C163 | C2 | semidirect |
| 81. Dic326 | #41 | semidirect |
| 82. D652 | SD16 | semidirect |
| 128. C163 | #3298 | semidirect |
| 136. #461 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782330 | 2 |
| #23782320 | 2 |
| #23782015 | 2 |
| #23781994 | 2 |
| #23781951 | 2 |
| #23781891 | 2 |
| #23781802 | 2 |
| C4×#14579687 | 2 |
| #23781730 | 2 |
| #103×D163 | 2 |
| #461×C163 | 2 |
| #3298 | 163 |