Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
586 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19098998 | C2 | semidirect |
| 2. C22×#14579102 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. C2×#19098370 | C2 | semidirect |
| 5. #23764310 | C2 | semidirect |
| 6. #23761489 | C2 | semidirect |
| 7. C79×#3155 | C2 | semidirect |
| 37. C2×D632 | D4 | semidirect |
| 43. #14579101 | D4 | semidirect |
| 47. C2×C79⋊C16 | D4 | semidirect |
| 209. #3155 | D79 | semidirect |
| 214. C79 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| C22×#14579102 | 2 |
| C2×#19098376 | 2 |
| C2×#19098370 | 2 |
| #23764310 | 2 |
| #23761489 | 2 |
| C79×#3155 | 2 |
| #13336 | 79 |