Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 3. Q16×C79⋊C8 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 5. #23761458 | C2 | semidirect |
| 7. C79×#2227 | C2 | semidirect |
| 60. Q16×C79 | SD16 | semidirect |
| 109. #2227 | D79 | semidirect |
| 116. C79 | #12419 | semidirect |
| 160. Q16 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765440 | 2 |
| #23762993 | 2 |
| Q16×C79⋊C8 | 2 |
| #23761463 | 2 |
| #23761458 | 2 |
| #23761447 | 2 |
| C79×#2227 | 2 |
| #12419 | 79 |