Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1074 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 219 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×#19098942 | C2 | semidirect |
| 2. C2×#19098853 | C2 | semidirect |
| 3. #23762545 | C2 | direct (N × H) |
| 4. C2×#19098312 | C2 | semidirect |
| 5. C2×D4⋊(C79⋊C8) | C2 | semidirect |
| 10. #19098942 | C22 | semidirect |
| 12. #19098853 | C22 | semidirect |
| 17. #19098312 | C22 | semidirect |
| 18. D4⋊(C79⋊C8) | C22 | semidirect |
| 153. C2×C79 | #1634 | semidirect |
| 162. C79 | C2×#1634 | semidirect |
| 308. C2 | #23762545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098942 | 2 |
| C2×#19098853 | 2 |
| #23762545 | 2 |
| C2×#19098312 | 2 |
| C2×D4⋊(C79⋊C8) | 2 |
| C2×#555×C79 | 2 |
| C2×#1634 | 79 |