Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765150 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. #23764191 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 67. #108×C79 | D4 | semidirect |
| 178. C2×#361 | D79 | semidirect |
| 182. C79 | #13417 | semidirect |
| 240. #108 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773881 | 2 |
| #23765150 | 2 |
| C2×#19098376 | 2 |
| #23765127 | 2 |
| #23764191 | 2 |
| #23761485 | 2 |
| C2×#361×C79 | 2 |
| #13417 | 79 |