Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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×#19098396 | C2 | semidirect |
| 2. #23765488 | C2 | semidirect |
| 4. #23761600 | C2 | semidirect |
| 5. #23761581 | C2 | semidirect |
| 6. #23761578 | C2 | semidirect |
| 7. C2×SD64×C79 | C2 | semidirect |
| 39. C32×C79 | D4 | semidirect |
| 96. C2×SD64 | D79 | semidirect |
| 103. C79 | #13699 | semidirect |
| 135. C32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098396 | 2 |
| #23765488 | 2 |
| #23765483 | 2 |
| #23761600 | 2 |
| #23761581 | 2 |
| #23761578 | 2 |
| C2×SD64×C79 | 2 |
| #13699 | 79 |