Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23782290 | C2 | semidirect |
| 2. #23781816 | C2 | semidirect |
| 4. #23781403 | C2 | semidirect |
| 5. #23781402 | C2 | semidirect |
| 6. #23781388 | C2 | semidirect |
| 7. #450×C163 | C2 | semidirect |
| 29. C2×Dic326 | D4 | semidirect |
| 40. C4⋊Dic163 | D4 | semidirect |
| 51. C2×Q8×C163 | D4 | semidirect |
| 59. C4⋊C4×C163 | D4 | semidirect |
| 65. C22×D163 | SD16 | semidirect |
| 130. C163 | #1596 | semidirect |
| 134. #450 | D163 | semidirect |
| 162. C2×Q8 | C22⋊D163 | semidirect |
| 184. C4⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782290 | 2 |
| #23781816 | 2 |
| #23781573 | 2 |
| #23781403 | 2 |
| #23781402 | 2 |
| #23781388 | 2 |
| #450×C163 | 2 |
| #1596 | 163 |