Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1198 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 183 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. #23773487 | C2 | semidirect |
| 2. #23766683 | C2 | semidirect |
| 3. #23762437 | C2 | semidirect |
| 4. #23762335 | C2 | semidirect |
| 5. #23761908 | C2 | semidirect |
| 6. #23761744 | C2 | semidirect |
| 7. C79×#3497 | C2 | semidirect |
| 199. #3497 | D79 | semidirect |
| 206. C79 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773487 | 2 |
| #23766683 | 2 |
| #23762437 | 2 |
| #23762335 | 2 |
| #23761908 | 2 |
| #23761744 | 2 |
| C79×#3497 | 2 |
| #18186 | 79 |