Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
938 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23761288 | C2 | semidirect |
| 4. #23761287 | C2 | semidirect |
| 5. C79×#1298 | C2 | semidirect |
| 176. D79 | #1298 | direct (N × H) |
| 181. #1298 | D79 | direct (N × H) |
| 182. C79 | C2×#1298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×D79 | 2 |
| C2×C22⋊C8×D79 | 2 |
| #23761288 | 2 |
| #23761287 | 2 |
| C79×#1298 | 2 |
| C2×#1298 | 79 |