Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23772439 | C2 | semidirect |
| 3. #23761736 | C2 | semidirect |
| 4. #23761727 | C2 | semidirect |
| 5. #23761307 | C2 | semidirect |
| 6. #23761305 | C2 | semidirect |
| 7. C79×#1462 | C2 | semidirect |
| 59. C22⋊(C79⋊C8) | D4 | semidirect |
| 79. C22⋊C8×C79 | D4 | semidirect |
| 264. #1462 | D79 | semidirect |
| 267. C79 | #9516 | semidirect |
| 335. C22⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772439 | 2 |
| #23768290 | 2 |
| #23761736 | 2 |
| #23761727 | 2 |
| #23761307 | 2 |
| #23761305 | 2 |
| C79×#1462 | 2 |
| #9516 | 79 |