Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19099004 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. C2×#19098371 | C2 | semidirect |
| 5. #23764316 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C22×SD32×C79 | C2 | semidirect |
| 53. #14579101 | D4 | semidirect |
| 68. C2×Q16×C79 | D4 | semidirect |
| 79. C2×C16×C79 | D4 | semidirect |
| 203. C22×SD32 | D79 | semidirect |
| 209. C79 | #13338 | semidirect |
| 248. C2×Q16 | C22⋊D79 | semidirect |
| 275. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773881 | 2 |
| C2×#19098376 | 2 |
| C2×#19098371 | 2 |
| #23764316 | 2 |
| #23761488 | 2 |
| C22×SD32×C79 | 2 |
| #13338 | 79 |