Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 770 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 |
|---|---|---|
| 3. #23764386 | C2 | semidirect |
| 4. #23763335 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 7. C2×#451×C79 | C2 | semidirect |
| 232. C2×#451 | D79 | semidirect |
| 238. C79 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| #23767054 | 2 |
| #23764386 | 2 |
| #23763335 | 2 |
| #23761969 | 2 |
| #23761246 | 2 |
| C2×#451×C79 | 2 |
| #9956 | 79 |