Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
648 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 648 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 |
|---|---|---|
| 2. #23766450 | C2 | semidirect |
| 3. #23764236 | C2 | semidirect |
| 4. #23761969 | C2 | semidirect |
| 5. C2×#19098298 | C2 | semidirect |
| 6. #23761280 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 12. #19098877 | C4 | semidirect |
| 15. #19098699 | C4 | semidirect |
| 31. C22×D316 | C2×C4 | semidirect |
| 49. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 79. C22⋊C8×C79 | C2×C4 | semidirect |
| 147. C22⋊C4×C79 | D8 | semidirect |
| 276. #1282 | D79 | semidirect |
| 277. C79 | #9277 | semidirect |
| 343. C22⋊C8 | C4×D79 | semidirect |
| 416. C22⋊C4 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774151 | 2 |
| #23766450 | 2 |
| #23764236 | 2 |
| #23761969 | 2 |
| C2×#19098298 | 2 |
| #23761280 | 2 |
| C79×#1282 | 2 |
| #9277 | 79 |