Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #23765147 | C2 | semidirect |
| 3. C2×#19098375 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. #23765127 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#1953 | C2 | semidirect |
| 65. #108×C79 | D4 | semidirect |
| 180. #1953 | D79 | semidirect |
| 182. C79 | #13417 | semidirect |
| 240. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773886 | 2 |
| #23765147 | 2 |
| C2×#19098375 | 2 |
| #23765127 | 2 |
| #23761486 | 2 |
| C79×#1953 | 2 |
| #13417 | 79 |