Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766510 | C2 | semidirect |
| 3. #23762023 | C2 | semidirect |
| 4. #23761909 | C2 | semidirect |
| 5. #23761907 | C2 | semidirect |
| 6. #23761294 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 12. #19098957 | C4 | semidirect |
| 13. #19098952 | C4 | semidirect |
| 43. #14579161 | C2×C4 | semidirect |
| 44. #14579158 | C2×C4 | semidirect |
| 76. #97×C79 | C2×C4 | semidirect |
| 233. #1300 | D79 | semidirect |
| 234. C79 | #9441 | semidirect |
| 298. #97 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773866 | 2 |
| #23766510 | 2 |
| #23762023 | 2 |
| #23761909 | 2 |
| #23761907 | 2 |
| #23761294 | 2 |
| C79×#1300 | 2 |
| #9441 | 79 |