Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23773971 | C2 | semidirect |
| 2. #23765566 | C2 | semidirect |
| 3. #23765560 | C2 | semidirect |
| 4. #23765498 | C2 | semidirect |
| 6. #23765464 | C2 | semidirect |
| 7. #23765458 | C2 | semidirect |
| 8. C2×Dic79⋊C16 | C2 | semidirect |
| 9. C79×#2216 | C2 | semidirect |
| 151. #2216 | D79 | semidirect |
| 156. C79 | #33816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773971 | 2 |
| #23765566 | 2 |
| #23765560 | 2 |
| #23765498 | 2 |
| #23765486 | 2 |
| #23765464 | 2 |
| #23765458 | 2 |
| C2×Dic79⋊C16 | 2 |
| C79×#2216 | 2 |
| #33816 | 79 |