Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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×#19098402 | C2 | semidirect |
| 2. #23765491 | C2 | semidirect |
| 4. #23761602 | C2 | semidirect |
| 5. #23761582 | C2 | semidirect |
| 6. #23761579 | C2 | semidirect |
| 7. C22×C32×C79 | C2 | semidirect |
| 39. C32×C79 | D4 | semidirect |
| 79. C22×C79 | SD64 | semidirect |
| 97. C22×C32 | D79 | semidirect |
| 103. C79 | #13696 | semidirect |
| 135. C32 | C22⋊D79 | semidirect |
| 178. C22 | #19098402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098402 | 2 |
| #23765491 | 2 |
| #23765486 | 2 |
| #23761602 | 2 |
| #23761582 | 2 |
| #23761579 | 2 |
| C22×C32×C79 | 2 |
| #13696 | 79 |