Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23772036 | C2 | semidirect |
| 3. #23761843 | C2 | semidirect |
| 4. #23761732 | C2 | semidirect |
| 5. #23761266 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 7. C79×#1490 | C2 | semidirect |
| 54. C4×C79⋊C8 | D4 | semidirect |
| 75. C4×C8×C79 | D4 | semidirect |
| 224. #1490 | D79 | semidirect |
| 228. C79 | #9494 | semidirect |
| 290. C4×C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772036 | 2 |
| #23768960 | 2 |
| #23761843 | 2 |
| #23761732 | 2 |
| #23761266 | 2 |
| #23761265 | 2 |
| C79×#1490 | 2 |
| #9494 | 79 |