Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #23765712 | C2 | semidirect |
| 2. #23765503 | C2 | semidirect |
| 3. #23761587 | C2 | semidirect |
| 4. #23761540 | C2 | semidirect |
| 5. C79×#3414 | C2 | semidirect |
| 6. C2×D1264 | C22 | semidirect |
| 10. #19098397 | C22 | semidirect |
| 11. #19098391 | C22 | semidirect |
| 35. Q32×C79 | D4 | semidirect |
| 39. D16×C79 | D4 | semidirect |
| 112. #3414 | D79 | semidirect |
| 117. C79 | #13667 | semidirect |
| 143. Q32 | C22⋊D79 | semidirect |
| 148. D16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765712 | 2 |
| #23765503 | 2 |
| #23761587 | 2 |
| #23761540 | 2 |
| C79×#3414 | 2 |
| #13667 | 79 |