Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
812 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19098701 | C2 | semidirect |
| 2. #23767059 | C2 | semidirect |
| 3. #23764237 | C2 | semidirect |
| 4. #23763336 | C2 | semidirect |
| 5. #23761968 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 250. C79 | #9948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098701 | 2 |
| #23767059 | 2 |
| #23764237 | 2 |
| #23763336 | 2 |
| #23761968 | 2 |
| #23761247 | 2 |
| C79×#3186 | 2 |
| #9948 | 79 |