Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
850 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 175 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. #23763517 | C2 | semidirect |
| 2. #23763253 | C2 | semidirect |
| 3. C2×#19098307 | C2 | semidirect |
| 21. C4⋊(C79⋊C8) | D4 | semidirect |
| 131. C79 | #9706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763517 | 2 |
| #23763253 | 2 |
| C2×#19098307 | 2 |
| C79×#2867 | 2 |
| #9706 | 79 |