Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #23781742 | C2 | semidirect |
| 3. D4×C163⋊C8 | C2 | semidirect |
| 4. #23781415 | C2 | semidirect |
| 5. #23781394 | C2 | semidirect |
| 6. #23781386 | C2 | semidirect |
| 7. D4⋊C8×C163 | C2 | semidirect |
| 55. D4×C163 | M16 | semidirect |
| 83. C163 | #1586 | semidirect |
| 90. D4⋊C8 | D163 | semidirect |
| 131. D4 | #14579682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579684 | 2 |
| #23781742 | 2 |
| D4×C163⋊C8 | 2 |
| #23781415 | 2 |
| #23781394 | 2 |
| #23781386 | 2 |
| D4⋊C8×C163 | 2 |
| #1586 | 163 |