Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23761353 | C2 | semidirect |
| 4. #23761352 | C2 | semidirect |
| 5. C79×#1328 | C2 | semidirect |
| 140. D79 | #1328 | direct (N × H) |
| 145. #1328 | D79 | direct (N × H) |
| 146. C79 | C2×#1328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #424×D79 | 2 |
| #349×D79 | 2 |
| #23761353 | 2 |
| #23761352 | 2 |
| C79×#1328 | 2 |
| C2×#1328 | 79 |