Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 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×#19098375 | C2 | semidirect |
| 3. #23765117 | C2 | semidirect |
| 4. #23765116 | C2 | semidirect |
| 5. #23764146 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 44. #14579095 | D4 | semidirect |
| 169. C2×#361 | D79 | semidirect |
| 174. C79 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098938 | 2 |
| C2×#19098375 | 2 |
| #23765117 | 2 |
| #23765116 | 2 |
| #23764146 | 2 |
| #23761481 | 2 |
| C2×#361×C79 | 2 |
| #13413 | 79 |