Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 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. C2×#19098377 | C2 | semidirect |
| 3. C2×#19098363 | C2 | semidirect |
| 4. C2×#19098348 | C2 | semidirect |
| 5. #23763465 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 7. C79×#2159 | C2 | semidirect |
| 61. M32×C79 | D4 | semidirect |
| 185. #2159 | D79 | semidirect |
| 191. C79 | #13387 | semidirect |
| 236. M32 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773049 | 2 |
| C2×#19098377 | 2 |
| C2×#19098363 | 2 |
| C2×#19098348 | 2 |
| #23763465 | 2 |
| #23761495 | 2 |
| C79×#2159 | 2 |
| #13387 | 79 |