Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. #23782463 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. #23781681 | C2 | semidirect |
| 4. #23781670 | C2 | semidirect |
| 5. #23781639 | C2 | semidirect |
| 6. #23781437 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 46. C2×C163⋊C8 | D4 | semidirect |
| 59. C2×Q8×C163 | D4 | semidirect |
| 67. C2×D4×C163 | D4 | semidirect |
| 73. M16×C163 | D4 | semidirect |
| 142. C163 | #2008 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 184. C2×Q8 | C22⋊D163 | semidirect |
| 195. C2×D4 | C22⋊D163 | semidirect |
| 208. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23782232 | 2 |
| #23781681 | 2 |
| #23781670 | 2 |
| #23781639 | 2 |
| #23781437 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #2008 | 163 |