Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23765762 | C2 | semidirect |
| 3. #23764320 | C2 | semidirect |
| 4. #23761842 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1505 | C2 | semidirect |
| 11. #19098850 | C4 | semidirect |
| 12. #19098755 | C4 | semidirect |
| 46. C4⋊(C79⋊C8) | C2×C4 | semidirect |
| 57. C4⋊Q8×C79 | C2×C4 | semidirect |
| 58. #127×C79 | C2×C4 | semidirect |
| 158. D316 | #104 | semidirect |
| 200. #1505 | D79 | semidirect |
| 204. C79 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D79 | semidirect |
| 233. #127 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773487 | 2 |
| #23765762 | 2 |
| #23764320 | 2 |
| #23761842 | 2 |
| #23761293 | 2 |
| #23761255 | 2 |
| C79×#1505 | 2 |
| #9325 | 79 |