Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23772274 | C2 | semidirect |
| 3. C2×#19098369 | C2 | semidirect |
| 4. C2×#19098363 | C2 | semidirect |
| 5. #23764308 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 12. #19099001 | C4 | semidirect |
| 41. C2×D632 | C2×C4 | semidirect |
| 66. M32×C79 | C2×C4 | semidirect |
| 194. #1387 | D79 | semidirect |
| 196. C79 | #13022 | semidirect |
| 245. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| #23772274 | 2 |
| C2×#19098369 | 2 |
| C2×#19098363 | 2 |
| #23764308 | 2 |
| #23761490 | 2 |
| C79×#1387 | 2 |
| #13022 | 79 |