Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23768406 | C2 | semidirect |
| 5. #23761280 | C2 | semidirect |
| 6. #23761268 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 28. C22×D316 | Q8 | semidirect |
| 42. C2×C4⋊Dic79 | Q8 | semidirect |
| 236. #1282 | D79 | semidirect |
| 237. C79 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768406 | 2 |
| #23764236 | 2 |
| #23761969 | 2 |
| C2×#19098298 | 2 |
| #23761280 | 2 |
| #23761268 | 2 |
| C79×#1282 | 2 |
| #10374 | 79 |