Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23773853 | C2 | semidirect |
| 2. #23769508 | C2 | semidirect |
| 3. #23762113 | C2 | semidirect |
| 4. #23761998 | C2 | semidirect |
| 5. #23761908 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 7. C79×#3213 | C2 | semidirect |
| 50. #14579072 | D4 | semidirect |
| 59. C4⋊Q8×C79 | D4 | semidirect |
| 60. #127×C79 | D4 | semidirect |
| 73. C4⋊C8×C79 | D4 | semidirect |
| 212. #3213 | D79 | semidirect |
| 219. C79 | #10088 | semidirect |
| 256. C4⋊Q8 | C22⋊D79 | semidirect |
| 262. #127 | C22⋊D79 | semidirect |
| 279. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773853 | 2 |
| #23769508 | 2 |
| #23762113 | 2 |
| #23761998 | 2 |
| #23761908 | 2 |
| #23761292 | 2 |
| C79×#3213 | 2 |
| #10088 | 79 |