Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23765637 | C2 | semidirect |
| 3. #23765547 | C2 | semidirect |
| 4. #23762914 | C2 | semidirect |
| 5. #23761442 | C2 | semidirect |
| 6. #23761359 | C2 | semidirect |
| 7. C79×#1333 | C2 | semidirect |
| 10. #19098968 | C22 | semidirect |
| 19. C4⋊(C79⋊C16) | C22 | semidirect |
| 25. #346×C79 | C22 | semidirect |
| 26. #334×C79 | C22 | semidirect |
| 99. D8×C79 | SD16 | semidirect |
| 172. #1333 | D79 | semidirect |
| 174. C79 | #12378 | semidirect |
| 191. #346 | C2×D79 | semidirect |
| 192. #334 | C2×D79 | semidirect |
| 253. D8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775010 | 2 |
| #23765637 | 2 |
| #23765547 | 2 |
| #23762914 | 2 |
| #23761442 | 2 |
| #23761359 | 2 |
| C79×#1333 | 2 |
| #12378 | 79 |