Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765687 | C2 | semidirect |
| 2. #23765537 | C2 | semidirect |
| 3. #23762923 | C2 | semidirect |
| 4. #23761452 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761358 | C2 | semidirect |
| 148. C79 | #12400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765687 | 2 |
| #23765537 | 2 |
| #23762923 | 2 |
| #23761452 | 2 |
| #23761367 | 2 |
| #23761358 | 2 |
| C79×#3355 | 2 |
| #12400 | 79 |