Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23782013 | C2 | semidirect |
| 2. #23781865 | C2 | semidirect |
| 4. #23781411 | C2 | semidirect |
| 5. Q8⋊(C163⋊C8) | C2 | semidirect |
| 6. D4⋊(C163⋊C8) | C2 | semidirect |
| 7. D4×Q8×C163 | C2 | semidirect |
| 65. Q8×C163 | D8 | semidirect |
| 67. D4×C163 | SD16 | semidirect |
| 99. C163 | #1627 | semidirect |
| 101. D4×Q8 | D163 | semidirect |
| 157. Q8 | #14579684 | semidirect |
| 164. D4 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782013 | 2 |
| #23781865 | 2 |
| #23781860 | 2 |
| #23781411 | 2 |
| Q8⋊(C163⋊C8) | 2 |
| D4⋊(C163⋊C8) | 2 |
| D4×Q8×C163 | 2 |
| #1627 | 163 |