Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #23781418 | C2 | semidirect |
| 5. #23781417 | C2 | semidirect |
| 6. #23781415 | C2 | semidirect |
| 7. #334×C163 | C2 | semidirect |
| 53. C163⋊C8 | M16 | semidirect |
| 60. C8×C163 | M16 | semidirect |
| 77. C163 | #1569 | semidirect |
| 85. #334 | D163 | semidirect |
| 138. C8 | #14579682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781721 | 2 |
| #23781687 | 2 |
| C4×#14579682 | 2 |
| #23781418 | 2 |
| #23781417 | 2 |
| #23781415 | 2 |
| #334×C163 | 2 |
| #1569 | 163 |