Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
270 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23781851 | C2 | semidirect |
| 2. #23781842 | C2 | semidirect |
| 3. #23781460 | C2 | semidirect |
| 4. #23781452 | C2 | semidirect |
| 5. H(3,𝔽4)×C163 | C2 | semidirect |
| 29. C24×C163 | D4 | semidirect |
| 31. C2×Q8×C163 | D4 | semidirect |
| 40. C22⋊C4×C163 | D4 | semidirect |
| 42. C42×C163 | D4 | semidirect |
| 88. C163 | #2199 | semidirect |
| 90. H(3,𝔽4) | D163 | semidirect |
| 108. C24 | C22⋊D163 | semidirect |
| 112. C2×Q8 | C22⋊D163 | semidirect |
| 129. C22⋊C4 | C22⋊D163 | semidirect |
| 131. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781851 | 2 |
| #23781842 | 2 |
| #23781460 | 2 |
| #23781452 | 2 |
| H(3,𝔽4)×C163 | 2 |
| #2199 | 163 |