Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1190 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 2. #23771883 | C2 | semidirect |
| 3. #23765053 | C2 | semidirect |
| 4. #23765039 | C2 | semidirect |
| 5. C79×#2884 | C2 | semidirect |
| 6. C22×Q8×D79 | C4 | semidirect |
| 12. #19099134 | C4 | semidirect |
| 14. #19099070 | C4 | semidirect |
| 16. #19099041 | C4 | semidirect |
| 183. #2884 | D79 | semidirect |
| 186. C79 | #33349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777048 | 2 |
| #23771883 | 2 |
| #23765053 | 2 |
| #23765039 | 2 |
| C79×#2884 | 2 |
| #33349 | 79 |