Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 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×#19098763 | C2 | semidirect |
| 3. #23762459 | C2 | direct (N × H) |
| 4. C2×#19098307 | C2 | semidirect |
| 5. C2×Q8⋊(C79⋊C8) | C2 | semidirect |
| 6. C2×#559×C79 | C2 | semidirect |
| 13. #19098763 | C22 | semidirect |
| 17. #19098307 | C22 | semidirect |
| 18. Q8⋊(C79⋊C8) | C22 | semidirect |
| 21. #559×C79 | C22 | semidirect |
| 161. C2×C79 | #1620 | semidirect |
| 165. C2×#559 | D79 | semidirect |
| 171. C79 | C2×#1620 | semidirect |
| 176. #559 | C2×D79 | semidirect |
| 326. C2 | #23762459 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098939 | 2 |
| C2×#19098763 | 2 |
| #23762459 | 2 |
| C2×#19098307 | 2 |
| C2×Q8⋊(C79⋊C8) | 2 |
| C2×#559×C79 | 2 |
| C2×#1620 | 79 |