Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781815 | C2 | semidirect |
| 2. #23781798 | C2 | semidirect |
| 3. #23781574 | C2 | semidirect |
| 4. #23781402 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781389 | C2 | semidirect |
| 7. #538×C163 | C2 | semidirect |
| 41. C2×Q8×C163 | D4 | semidirect |
| 45. C2×D4×C163 | D4 | semidirect |
| 51. C4⋊C4×C163 | D4 | semidirect |
| 52. C4⋊C4×C163 | D4 | semidirect |
| 135. C163 | #1600 | semidirect |
| 137. #538 | D163 | semidirect |
| 165. C2×Q8 | C22⋊D163 | semidirect |
| 175. C2×D4 | C22⋊D163 | semidirect |
| 186. C4⋊C4 | C22⋊D163 | semidirect |
| 187. C4⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781815 | 2 |
| #23781798 | 2 |
| #23781574 | 2 |
| #23781402 | 2 |
| #23781399 | 2 |
| #23781389 | 2 |
| #538×C163 | 2 |
| #1600 | 163 |