Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23781569 | C2 | semidirect |
| 3. #23781557 | C2 | semidirect |
| 4. #23781554 | C2 | semidirect |
| 6. #23781539 | C2 | semidirect |
| 7. C4×C4⋊Dic163 | C2 | semidirect |
| 8. #23781512 | C2 | semidirect |
| 9. #383×C163 | C2 | semidirect |
| 13. #19104723 | C4 | semidirect |
| 34. C2×Dic326 | C2×C4 | semidirect |
| 48. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 49. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 58. C42×C163 | C2×C4 | semidirect |
| 118. C163 | #2337 | semidirect |
| 126. #383 | D163 | semidirect |
| 177. C42 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104723 | 2 |
| #23781569 | 2 |
| #23781557 | 2 |
| #23781554 | 2 |
| #23781543 | 2 |
| #23781539 | 2 |
| C4×C4⋊Dic163 | 2 |
| #23781512 | 2 |
| #383×C163 | 2 |
| #2337 | 163 |