Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23765625 | C2 | semidirect |
| 3. #23762760 | C2 | semidirect |
| 4. #23761455 | C2 | semidirect |
| 5. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761361 | C2 | semidirect |
| 7. Q8×D8×C79 | C2 | semidirect |
| 72. D8×C79 | SD16 | semidirect |
| 92. Q8×C79 | D16 | semidirect |
| 137. Q8×D8 | D79 | semidirect |
| 144. C79 | #12352 | semidirect |
| 206. D8 | #11929611 | semidirect |
| 229. Q8 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765625 | 2 |
| #23765435 | 2 |
| #23762760 | 2 |
| #23761455 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761361 | 2 |
| Q8×D8×C79 | 2 |
| #12352 | 79 |