Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23774320 | C2 | semidirect |
| 2. #23771795 | C2 | semidirect |
| 3. #23764228 | C2 | semidirect |
| 4. #23762067 | C2 | semidirect |
| 5. C79×#1276 | C2 | semidirect |
| 26. #14579161 | D4 | semidirect |
| 34. #14579158 | D4 | semidirect |
| 44. C4⋊C8×C79 | D4 | semidirect |
| 78. C42×C79 | D8 | semidirect |
| 140. #1276 | D79 | semidirect |
| 141. C79 | #10280 | semidirect |
| 178. C4⋊C8 | D316 | semidirect |
| 214. C42 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774320 | 2 |
| #23771795 | 2 |
| #23764228 | 2 |
| #23762067 | 2 |
| C79×#1276 | 2 |
| #10280 | 79 |