Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
538 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4×C22⋊(C79⋊C8) | C2 | semidirect |
| 3. #23761225 | C2 | semidirect |
| 4. #23761220 | C2 | semidirect |
| 5. C79×#1817 | C2 | semidirect |
| 194. #1817 | D79 | semidirect |
| 198. C79 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771701 | 2 |
| C4×C22⋊(C79⋊C8) | 2 |
| #23761225 | 2 |
| #23761220 | 2 |
| C79×#1817 | 2 |
| #7670 | 79 |