Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19098400 | C2 | semidirect |
| 3. #23761581 | C2 | semidirect |
| 4. C22⋊(C79⋊C32) | C2 | semidirect |
| 5. C22×Q32×C79 | C2 | semidirect |
| 31. Q32×C79 | D4 | semidirect |
| 76. C22×C79 | SD64 | semidirect |
| 92. C22×Q32 | D79 | semidirect |
| 97. C79 | #13662 | semidirect |
| 119. Q32 | C22⋊D79 | semidirect |
| 171. C22 | #19098400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098400 | 2 |
| #23765486 | 2 |
| #23761581 | 2 |
| C22⋊(C79⋊C32) | 2 |
| C22×Q32×C79 | 2 |
| #13662 | 79 |