Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 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. #23774405 | C2 | semidirect |
| 2. #23773774 | C2 | semidirect |
| 4. #23761999 | C2 | semidirect |
| 5. #23761913 | C2 | semidirect |
| 6. #23761292 | C2 | semidirect |
| 7. C79×#1555 | C2 | semidirect |
| 37. #14579161 | D4 | semidirect |
| 38. #14579161 | D4 | semidirect |
| 59. #14579072 | D4 | semidirect |
| 72. C4⋊C8×C79 | D4 | semidirect |
| 204. #1555 | D79 | semidirect |
| 208. C79 | #10096 | semidirect |
| 265. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774405 | 2 |
| #23773774 | 2 |
| #23769507 | 2 |
| #23761999 | 2 |
| #23761913 | 2 |
| #23761292 | 2 |
| C79×#1555 | 2 |
| #10096 | 79 |