Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23776490 | C2 | semidirect |
| 2. #23765664 | C2 | semidirect |
| 3. #23765432 | C2 | semidirect |
| 4. #23761442 | C2 | semidirect |
| 5. #23761382 | C2 | semidirect |
| 6. #23761366 | C2 | semidirect |
| 7. C79×#1688 | C2 | semidirect |
| 165. #1688 | D79 | semidirect |
| 169. C79 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776490 | 2 |
| #23765664 | 2 |
| #23765432 | 2 |
| #23761442 | 2 |
| #23761382 | 2 |
| #23761366 | 2 |
| C79×#1688 | 2 |
| #12336 | 79 |