Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19098704 | C2 | semidirect |
| 3. C2×#19098701 | C2 | semidirect |
| 4. #23763323 | C2 | semidirect |
| 5. #23761761 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 7. C79×#1471 | C2 | semidirect |
| 230. #1471 | D79 | semidirect |
| 232. C79 | #9988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774197 | 2 |
| C2×#19098704 | 2 |
| C2×#19098701 | 2 |
| #23763323 | 2 |
| #23761761 | 2 |
| #23761288 | 2 |
| C79×#1471 | 2 |
| #9988 | 79 |