Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23765673 | C2 | semidirect |
| 3. #23765628 | C2 | semidirect |
| 4. #23762998 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 56. C79⋊C16 | SD16 | semidirect |
| 111. C79 | #12508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765673 | 2 |
| #23765655 | 2 |
| #23765628 | 2 |
| #23762998 | 2 |
| #23762989 | 2 |
| #23761316 | 2 |
| C79×#2240 | 2 |
| #12508 | 79 |