Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19098380 | C2 | semidirect |
| 4. #23765121 | C2 | semidirect |
| 6. #23764148 | C2 | semidirect |
| 7. C79×#1376 | C2 | semidirect |
| 166. #1376 | D79 | semidirect |
| 167. C79 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098947 | 2 |
| C2×#19098380 | 2 |
| C2×#19098377 | 2 |
| #23765121 | 2 |
| #23765117 | 2 |
| #23764148 | 2 |
| C79×#1376 | 2 |
| #13414 | 79 |