Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23765997 | C2 | semidirect |
| 3. #23761968 | C2 | semidirect |
| 4. C2×#19098286 | C2 | semidirect |
| 5. #23761268 | C2 | semidirect |
| 6. #23761267 | C2 | semidirect |
| 7. C79×#1519 | C2 | semidirect |
| 11. #19098489 | C4 | semidirect |
| 13. #19098471 | C4 | semidirect |
| 53. C79⋊#95 | D4 | semidirect |
| 68. #95×C79 | D4 | semidirect |
| 254. #1519 | D79 | semidirect |
| 258. C79 | #9205 | semidirect |
| 319. #95 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769136 | 2 |
| #23765997 | 2 |
| #23761968 | 2 |
| C2×#19098286 | 2 |
| #23761268 | 2 |
| #23761267 | 2 |
| C79×#1519 | 2 |
| #9205 | 79 |