Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
322 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23765620 | C2 | semidirect |
| 3. #23765615 | C2 | semidirect |
| 4. #23764953 | C2 | semidirect |
| 5. #23761389 | C2 | semidirect |
| 6. #23761386 | C2 | semidirect |
| 7. C79×#1321 | C2 | semidirect |
| 160. #1321 | D79 | semidirect |
| 161. C79 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774312 | 2 |
| #23765620 | 2 |
| #23765615 | 2 |
| #23764953 | 2 |
| #23761389 | 2 |
| #23761386 | 2 |
| C79×#1321 | 2 |
| #12303 | 79 |