Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23766465 | C2 | semidirect |
| 2. #23764328 | C2 | semidirect |
| 3. C2×#19098307 | C2 | semidirect |
| 4. #23761240 | C2 | semidirect |
| 18. #493×C79 | C4 | semidirect |
| 46. #127×C79 | C2×C4 | semidirect |
| 50. C4×C8×C79 | C2×C4 | semidirect |
| 61. C4⋊Dic79 | D8 | semidirect |
| 175. C79 | #9061 | semidirect |
| 181. #493 | Dic79 | semidirect |
| 204. #127 | C2×Dic79 | semidirect |
| 219. C4×C8 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766465 | 2 |
| #23764328 | 2 |
| C2×#19098307 | 2 |
| #23761240 | 2 |
| C2×#493×C79 | 2 |
| #9061 | 79 |