Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782389 | C2 | semidirect |
| 3. #23782002 | C2 | semidirect |
| 4. #23781992 | C2 | semidirect |
| 5. #23781947 | C2 | semidirect |
| 6. #23781942 | C2 | semidirect |
| 7. #23781912 | C2 | semidirect |
| 8. C4×#14579688 | C2 | semidirect |
| 9. #23781744 | C2 | semidirect |
| 10. #23781706 | C2 | semidirect |
| 11. #500×C163 | C2 | semidirect |
| 99. C8×C163 | #41 | semidirect |
| 122. C163 | #3353 | semidirect |
| 126. #500 | D163 | semidirect |
| 222. C8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782389 | 2 |
| #23782318 | 2 |
| #23782002 | 2 |
| #23781992 | 2 |
| #23781947 | 2 |
| #23781942 | 2 |
| #23781912 | 2 |
| C4×#14579688 | 2 |
| #23781744 | 2 |
| #23781706 | 2 |
| #500×C163 | 2 |
| #3353 | 163 |