Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23774387 | C2 | semidirect |
| 2. #23773852 | C2 | semidirect |
| 3. #23769508 | C2 | semidirect |
| 4. #23762113 | C2 | semidirect |
| 5. #23761909 | C2 | semidirect |
| 6. #23761294 | C2 | semidirect |
| 7. C79×#1527 | C2 | semidirect |
| 41. #14579161 | D4 | semidirect |
| 46. #14579158 | D4 | semidirect |
| 56. C4⋊(C79⋊C8) | D4 | semidirect |
| 76. #97×C79 | D4 | semidirect |
| 216. #1527 | D79 | semidirect |
| 219. C79 | #10088 | semidirect |
| 286. #97 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774387 | 2 |
| #23773852 | 2 |
| #23769508 | 2 |
| #23762113 | 2 |
| #23761909 | 2 |
| #23761294 | 2 |
| C79×#1527 | 2 |
| #10088 | 79 |