Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23771828 | C2 | semidirect |
| 3. #23762012 | C2 | semidirect |
| 4. #23761816 | C2 | semidirect |
| 5. #23761300 | C2 | semidirect |
| 6. #23761273 | C2 | semidirect |
| 7. C79×#1488 | C2 | semidirect |
| 204. #1488 | D79 | semidirect |
| 208. C79 | #9311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773551 | 2 |
| #23771828 | 2 |
| #23762012 | 2 |
| #23761816 | 2 |
| #23761300 | 2 |
| #23761273 | 2 |
| C79×#1488 | 2 |
| #9311 | 79 |