Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #23762993 | C2 | semidirect |
| 3. D8×C79⋊C8 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 5. #23761455 | C2 | semidirect |
| 6. #23761447 | C2 | semidirect |
| 7. C79×#2224 | C2 | semidirect |
| 63. D8×C79 | SD16 | semidirect |
| 96. C79⋊C8 | D16 | semidirect |
| 117. #2224 | D79 | semidirect |
| 124. C79 | #12416 | semidirect |
| 174. D8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765435 | 2 |
| #23762993 | 2 |
| D8×C79⋊C8 | 2 |
| #23761463 | 2 |
| #23761455 | 2 |
| #23761447 | 2 |
| C79×#2224 | 2 |
| #12416 | 79 |