Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
676 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#19098996 | C2 | semidirect |
| 2. #23775120 | C2 | semidirect |
| 3. #23765488 | C2 | semidirect |
| 4. #23765442 | C2 | semidirect |
| 5. #23765339 | C2 | semidirect |
| 6. C4×D1264 | C2 | semidirect |
| 7. C16×D316 | C2 | semidirect |
| 8. C79×#2247 | C2 | semidirect |
| 42. D1264 | D4 | semidirect |
| 121. C4×C79 | #508 | semidirect |
| 134. #2247 | D79 | semidirect |
| 140. C79 | #33849 | semidirect |
| 255. C4 | #19098996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098996 | 2 |
| #23775120 | 2 |
| #23765488 | 2 |
| #23765442 | 2 |
| #23765339 | 2 |
| C4×D1264 | 2 |
| C16×D316 | 2 |
| C79×#2247 | 2 |
| #33849 | 79 |