Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 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. #23774403 | C2 | semidirect |
| 2. #23773774 | C2 | semidirect |
| 3. #23762114 | C2 | semidirect |
| 4. #23761998 | C2 | semidirect |
| 5. #23761911 | C2 | semidirect |
| 6. #23761293 | C2 | semidirect |
| 34. #14579161 | D4 | semidirect |
| 35. #14579161 | D4 | semidirect |
| 43. C4⋊(C79⋊C8) | D4 | semidirect |
| 52. #14579072 | D4 | semidirect |
| 208. C79 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774403 | 2 |
| #23773774 | 2 |
| #23762114 | 2 |
| #23761998 | 2 |
| #23761911 | 2 |
| #23761293 | 2 |
| C79×#2657 | 2 |
| #10096 | 79 |