Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782215 | C2 | semidirect |
| 2. #23782070 | C2 | semidirect |
| 3. #23782042 | C2 | semidirect |
| 4. #23782012 | C2 | semidirect |
| 5. #23781901 | C2 | semidirect |
| 6. C4×D1304 | C2 | semidirect |
| 7. C2×C4×C8×C163 | C2 | semidirect |
| 57. C2×C4×C163 | D8 | semidirect |
| 65. C8×C163 | #41 | semidirect |
| 85. C163 | #3169 | semidirect |
| 93. C2×C4×C8 | D163 | semidirect |
| 143. C2×C4 | D1304 | semidirect |
| 151. C8 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| #23782070 | 2 |
| #23782042 | 2 |
| #23782012 | 2 |
| #23781901 | 2 |
| C4×D1304 | 2 |
| C2×C4×C8×C163 | 2 |
| #3169 | 163 |