Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23765194 | C2 | semidirect |
| 2. C2×#19098376 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23765028 | C2 | semidirect |
| 5. #23763450 | C2 | semidirect |
| 6. #23761513 | C2 | semidirect |
| 171. C79 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765194 | 2 |
| C2×#19098376 | 2 |
| #23765028 | 2 |
| #23763450 | 2 |
| #23761513 | 2 |
| C2×#472×C79 | 2 |
| #13389 | 79 |