Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
308 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765195 | C2 | semidirect |
| 2. #23765172 | C2 | semidirect |
| 5. #23763523 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 138. C79 | #13523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765195 | 2 |
| #23765172 | 2 |
| C2×#19098376 | 2 |
| #23764311 | 2 |
| #23763523 | 2 |
| #23761485 | 2 |
| C79×#2140 | 2 |
| #13523 | 79 |