Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 368 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. #23782223 | C2 | semidirect |
| 2. #23781801 | C2 | semidirect |
| 3. #23781798 | C2 | semidirect |
| 4. #23781575 | C2 | semidirect |
| 5. #23781398 | C2 | semidirect |
| 6. #23781388 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 9. C22×D652 | C22 | semidirect |
| 23. C22⋊(C163⋊C8) | C22 | semidirect |
| 25. C22⋊C8×C163 | C22 | semidirect |
| 26. #95×C163 | C22 | semidirect |
| 37. C2×D652 | D4 | semidirect |
| 48. C4⋊Dic163 | D4 | semidirect |
| 57. C2×D4×C163 | D4 | semidirect |
| 61. C4⋊C4×C163 | D4 | semidirect |
| 78. C22×D163 | D8 | semidirect |
| 147. C163 | #1595 | semidirect |
| 154. #327 | D163 | semidirect |
| 173. C22⋊C8 | C2×D163 | semidirect |
| 174. #95 | C2×D163 | semidirect |
| 192. C2×D4 | D652 | semidirect |
| 203. C4⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782223 | 2 |
| #23781801 | 2 |
| #23781798 | 2 |
| #23781575 | 2 |
| #23781398 | 2 |
| #23781388 | 2 |
| #327×C163 | 2 |
| #1595 | 163 |