Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 1. #23765623 | C2 | semidirect |
| 2. #23763018 | C2 | semidirect |
| 3. C8×C79⋊C16 | C2 | semidirect |
| 70. C79 | #12509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765623 | 2 |
| #23763018 | 2 |
| C8×C79⋊C16 | 2 |
| C79×#1712 | 2 |
| #12509 | 79 |