Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 366 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 |
|---|---|---|
| 2. #23764388 | C2 | semidirect |
| 3. #23762191 | C2 | semidirect |
| 4. #23762073 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 163. C79 | #10491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774525 | 2 |
| #23764388 | 2 |
| #23762191 | 2 |
| #23762073 | 2 |
| #23761817 | 2 |
| #23761289 | 2 |
| C79×#1560 | 2 |
| #10491 | 79 |