Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#19098402 | C2 | semidirect |
| 2. C2×#19098401 | C2 | semidirect |
| 3. C2×#19098398 | C2 | semidirect |
| 4. #23765658 | C2 | semidirect |
| 5. #23765648 | C2 | semidirect |
| 6. #23761533 | C2 | semidirect |
| 7. C2×D32×C79 | C2 | semidirect |
| 37. C79⋊C32 | D4 | semidirect |
| 45. C32×C79 | D4 | semidirect |
| 106. C2×D32 | D79 | semidirect |
| 110. C79 | #13729 | semidirect |
| 148. C32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098402 | 2 |
| C2×#19098401 | 2 |
| C2×#19098398 | 2 |
| #23765658 | 2 |
| #23765648 | 2 |
| #23761533 | 2 |
| C2×D32×C79 | 2 |
| #13729 | 79 |