Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
182 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23782012 | C2 | semidirect |
| 2. #23781870 | C2 | semidirect |
| 4. #23781418 | C2 | semidirect |
| 5. #23781410 | C2 | semidirect |
| 6. #23781408 | C2 | semidirect |
| 7. C8×D4×C163 | C2 | semidirect |
| 84. C163 | #1681 | semidirect |
| 89. C8×D4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782012 | 2 |
| #23781870 | 2 |
| #23781860 | 2 |
| #23781418 | 2 |
| #23781410 | 2 |
| #23781408 | 2 |
| C8×D4×C163 | 2 |
| #1681 | 163 |