Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #23765695 | C2 | semidirect |
| 3. #23761543 | C2 | semidirect |
| 4. C4×C79⋊C32 | C2 | semidirect |
| 5. C79×#1422 | C2 | semidirect |
| 67. #1422 | D79 | semidirect |
| 70. C79 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765695 | 2 |
| #23765238 | 2 |
| #23761543 | 2 |
| C4×C79⋊C32 | 2 |
| C79×#1422 | 2 |
| #13647 | 79 |