Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
350 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 4. #23761456 | C2 | semidirect |
| 5. #23761455 | C2 | semidirect |
| 6. #23761454 | C2 | semidirect |
| 7. C79×#1364 | C2 | semidirect |
| 129. D79 | #1364 | direct (N × H) |
| 136. #1364 | D79 | direct (N × H) |
| 137. C79 | C2×#1364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D79 | 2 |
| C4⋊C16×D79 | 2 |
| #335×D79 | 2 |
| #23761456 | 2 |
| #23761455 | 2 |
| #23761454 | 2 |
| C79×#1364 | 2 |
| C2×#1364 | 79 |