Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19098376 | C2 | semidirect |
| 4. #23765115 | C2 | semidirect |
| 5. #23764149 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 7. C79×#2140 | C2 | semidirect |
| 61. #107×C79 | D4 | semidirect |
| 171. #2140 | D79 | semidirect |
| 174. C79 | #13413 | semidirect |
| 225. #107 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098938 | 2 |
| C2×#19098377 | 2 |
| C2×#19098376 | 2 |
| #23765115 | 2 |
| #23764149 | 2 |
| #23761481 | 2 |
| C79×#2140 | 2 |
| #13413 | 79 |