Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23765567 | C2 | semidirect |
| 3. #23765562 | C2 | semidirect |
| 6. #23765449 | C2 | semidirect |
| 7. #23765448 | C2 | semidirect |
| 147. C79 | #33827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774052 | 2 |
| #23765567 | 2 |
| #23765562 | 2 |
| #23765508 | 2 |
| #23765489 | 2 |
| #23765449 | 2 |
| #23765448 | 2 |
| #23765160 | 2 |
| C79×#2219 | 2 |
| #33827 | 79 |