Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23761348 | C2 | semidirect |
| 4. #23761330 | C2 | semidirect |
| 35. #123×C79 | C8 | semidirect |
| 85. C22×C4×C79 | C2×C8 | semidirect |
| 100. C22⋊C4×C79 | C2×C8 | semidirect |
| 192. C79 | #11474 | semidirect |
| 217. #123 | C79⋊C8 | semidirect |
| 269. C22×C4 | C2×C79⋊C8 | semidirect |
| 287. C22⋊C4 | C2×C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761721 | 2 |
| #23761718 | 2 |
| #23761348 | 2 |
| #23761330 | 2 |
| C79×#2322 | 2 |
| #11474 | 79 |