Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23764316 | C2 | semidirect |
| 5. #23761508 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C2×#358×C79 | C2 | semidirect |
| 11. #19099004 | C4 | semidirect |
| 47. #14579101 | C2×C4 | semidirect |
| 64. C2×Q16×C79 | C2×C4 | semidirect |
| 185. C2×#358 | D79 | semidirect |
| 189. C79 | #13023 | semidirect |
| 222. C2×Q16 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23772274 | 2 |
| C2×#19098371 | 2 |
| #23764316 | 2 |
| #23761508 | 2 |
| #23761488 | 2 |
| C2×#358×C79 | 2 |
| #13023 | 79 |