Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
888 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19098356 | C2 | semidirect |
| 3. #23763348 | C2 | semidirect |
| 4. #23761519 | C2 | semidirect |
| 19. #453×C79 | C4 | semidirect |
| 42. H(5,𝔽2)×C79 | C2×C4 | semidirect |
| 61. #100×C79 | C2×C4 | semidirect |
| 109. C2×D4×C79 | C22⋊C4 | semidirect |
| 123. C42×C79 | C22⋊C4 | semidirect |
| 225. C79 | #13047 | semidirect |
| 231. #453 | Dic79 | semidirect |
| 245. H(5,𝔽2) | C2×Dic79 | semidirect |
| 276. #100 | C2×Dic79 | semidirect |
| 312. C2×D4 | C22⋊Dic79 | semidirect |
| 343. C42 | C22⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766465 | 2 |
| C2×#19098356 | 2 |
| #23763348 | 2 |
| #23761519 | 2 |
| C2×#453×C79 | 2 |
| #13047 | 79 |