Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 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. #23782216 | C2 | semidirect |
| 2. #23782042 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781902 | C2 | semidirect |
| 5. #23781747 | C2 | semidirect |
| 6. C4×C8×D163 | C2 | semidirect |
| 7. #500×C163 | C2 | semidirect |
| 58. C4×D163 | D8 | semidirect |
| 65. C8×C163 | #41 | semidirect |
| 85. C163 | #3169 | semidirect |
| 88. #500 | D163 | semidirect |
| 151. C8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| #23782042 | 2 |
| #23782013 | 2 |
| #23781902 | 2 |
| #23781747 | 2 |
| C4×C8×D163 | 2 |
| #500×C163 | 2 |
| #3169 | 163 |