Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23772423 | C2 | semidirect |
| 3. #23763389 | C2 | semidirect |
| 4. #23761826 | C2 | semidirect |
| 5. #23761824 | C2 | semidirect |
| 6. #23761258 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 56. C4×C79⋊C8 | D4 | semidirect |
| 65. C4×C8×C79 | D4 | semidirect |
| 216. #1286 | D79 | semidirect |
| 217. C79 | #9485 | semidirect |
| 274. C4×C8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772423 | 2 |
| #23768302 | 2 |
| #23763389 | 2 |
| #23761826 | 2 |
| #23761824 | 2 |
| #23761258 | 2 |
| C79×#1286 | 2 |
| #9485 | 79 |