Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23776502 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23763447 | C2 | semidirect |
| 5. #23761515 | C2 | semidirect |
| 6. #23761514 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 41. #14579101 | D4 | semidirect |
| 62. M32×C79 | D4 | semidirect |
| 172. C2×#361 | D79 | semidirect |
| 176. C79 | #13079 | semidirect |
| 222. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776502 | 2 |
| #23773044 | 2 |
| C2×#19098376 | 2 |
| #23763447 | 2 |
| #23761515 | 2 |
| #23761514 | 2 |
| C2×#361×C79 | 2 |
| #13079 | 79 |