Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×Dic326 | C2 | semidirect |
| 2. #23781981 | C2 | semidirect |
| 3. #23781947 | C2 | semidirect |
| 4. #23781862 | C2 | semidirect |
| 5. #23781803 | C2 | semidirect |
| 6. C4×#14579687 | C2 | semidirect |
| 7. #23781718 | C2 | semidirect |
| 66. Dic326 | #41 | semidirect |
| 83. C2×C4×C163 | SD16 | semidirect |
| 111. C163 | #3103 | semidirect |
| 194. C2×C4 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic326 | 2 |
| #23781981 | 2 |
| #23781947 | 2 |
| #23781862 | 2 |
| #23781803 | 2 |
| C4×#14579687 | 2 |
| #23781718 | 2 |
| #532×C163 | 2 |
| #3103 | 163 |