Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
950 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23774315 | C2 | semidirect |
| 2. #23771795 | C2 | semidirect |
| 3. #23762069 | C2 | semidirect |
| 4. #23761233 | C2 | semidirect |
| 5. C79×#1962 | C2 | semidirect |
| 31. C4⋊(C79⋊C8) | D4 | semidirect |
| 37. C4⋊Q8×C79 | D4 | semidirect |
| 38. #127×C79 | D4 | semidirect |
| 78. C42×C79 | D8 | semidirect |
| 138. #1962 | D79 | semidirect |
| 141. C79 | #10280 | semidirect |
| 162. C4⋊Q8 | D316 | semidirect |
| 170. #127 | D316 | semidirect |
| 214. C42 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774315 | 2 |
| #23771795 | 2 |
| #23762069 | 2 |
| #23761233 | 2 |
| C79×#1962 | 2 |
| #10280 | 79 |