Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23781798 | C2 | semidirect |
| 2. #23781574 | C2 | semidirect |
| 3. #23781399 | C2 | semidirect |
| 4. #23781389 | C2 | semidirect |
| 5. #534×C163 | C2 | semidirect |
| 6. C22×D652 | C22 | semidirect |
| 11. C22⋊(C163⋊C8) | C22 | semidirect |
| 12. C163⋊#95 | C22 | semidirect |
| 36. C2×D4×C163 | D4 | semidirect |
| 41. C4⋊C4×C163 | D4 | semidirect |
| 67. C23×C163 | D8 | semidirect |
| 113. C163 | #1595 | semidirect |
| 115. #534 | D163 | semidirect |
| 146. C2×D4 | C22⋊D163 | semidirect |
| 154. C4⋊C4 | C22⋊D163 | semidirect |
| 174. C23 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781798 | 2 |
| #23781574 | 2 |
| #23781399 | 2 |
| #23781389 | 2 |
| #534×C163 | 2 |
| #1595 | 163 |