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×#19098377 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. #23763447 | C2 | semidirect |
| 6. #23761516 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 47. #14579101 | D4 | semidirect |
| 60. M32×C79 | D4 | semidirect |
| 175. #1389 | D79 | semidirect |
| 176. C79 | #13079 | semidirect |
| 222. M32 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776502 | 2 |
| #23773049 | 2 |
| C2×#19098377 | 2 |
| C2×#19098375 | 2 |
| #23763447 | 2 |
| #23761516 | 2 |
| C79×#1389 | 2 |
| #13079 | 79 |