Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23762170 | C2 | semidirect |
| 3. #23762050 | C2 | semidirect |
| 4. #23761959 | C2 | semidirect |
| 5. #23761721 | C2 | semidirect |
| 6. #23761258 | C2 | semidirect |
| 7. C79×#1804 | C2 | semidirect |
| 193. #1804 | D79 | semidirect |
| 199. C79 | #10465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772864 | 2 |
| #23762170 | 2 |
| #23762050 | 2 |
| #23761959 | 2 |
| #23761721 | 2 |
| #23761258 | 2 |
| C79×#1804 | 2 |
| #10465 | 79 |