Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
558 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19099006 | C2 | semidirect |
| 3. C2×#19098374 | C2 | semidirect |
| 4. #23764271 | C2 | semidirect |
| 5. C79×#1377 | C2 | semidirect |
| 35. C2×Dic316 | D4 | semidirect |
| 55. M32×C79 | D4 | semidirect |
| 158. #1377 | D79 | semidirect |
| 159. C79 | #13342 | semidirect |
| 206. M32 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099006 | 2 |
| #23773846 | 2 |
| C2×#19098374 | 2 |
| #23764271 | 2 |
| C79×#1377 | 2 |
| #13342 | 79 |