Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19104756 | C2 | semidirect |
| 2. #23782337 | C2 | semidirect |
| 3. #23782319 | C2 | semidirect |
| 4. #23782038 | C2 | semidirect |
| 5. #23781895 | C2 | semidirect |
| 6. #23781875 | C2 | semidirect |
| 7. #23781860 | C2 | semidirect |
| 8. #23781830 | C2 | semidirect |
| 9. #23781811 | C2 | semidirect |
| 10. C8×D652 | C2 | semidirect |
| 11. C4×SD16×C163 | C2 | semidirect |
| 73. SD16×C163 | D4 | semidirect |
| 129. C4×C163 | #135 | semidirect |
| 140. C163 | #3284 | semidirect |
| 151. C4×SD16 | D163 | semidirect |
| 204. SD16 | D652 | semidirect |
| 272. C4 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| #23782337 | 2 |
| #23782319 | 2 |
| #23782038 | 2 |
| #23781895 | 2 |
| #23781875 | 2 |
| #23781860 | 2 |
| #23781830 | 2 |
| #23781811 | 2 |
| C8×D652 | 2 |
| C4×SD16×C163 | 2 |
| #3284 | 163 |