Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 4. C2×#19098368 | C2 | semidirect |
| 5. #23764315 | C2 | semidirect |
| 6. #23761509 | C2 | semidirect |
| 7. C79×#1379 | C2 | semidirect |
| 12. #19099006 | C4 | semidirect |
| 39. C2×Dic316 | C2×C4 | semidirect |
| 65. M32×C79 | C2×C4 | semidirect |
| 188. #1379 | D79 | semidirect |
| 189. C79 | #13023 | semidirect |
| 238. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099006 | 2 |
| #23772277 | 2 |
| C2×#19098371 | 2 |
| C2×#19098368 | 2 |
| #23764315 | 2 |
| #23761509 | 2 |
| C79×#1379 | 2 |
| #13023 | 79 |