Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23782148 | C2 | semidirect |
| 3. #23781671 | C2 | semidirect |
| 4. #23781567 | C2 | semidirect |
| 5. #23781433 | C2 | semidirect |
| 6. #23781425 | C2 | semidirect |
| 7. C2×#104×C163 | C2 | semidirect |
| 10. #19104760 | C4 | semidirect |
| 34. C2×D652 | C2×C4 | semidirect |
| 40. #14579683 | C2×C4 | semidirect |
| 85. Q8×C163 | C22⋊C4 | semidirect |
| 89. D4×C163 | C22⋊C4 | semidirect |
| 132. C163 | #1883 | semidirect |
| 136. C2×#104 | D163 | semidirect |
| 208. Q8 | (C2×D163)⋊C4 | semidirect |
| 216. D4 | (C2×D163)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| #23782148 | 2 |
| #23781671 | 2 |
| #23781567 | 2 |
| #23781433 | 2 |
| #23781425 | 2 |
| C2×#104×C163 | 2 |
| #1883 | 163 |