Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 4. #23761458 | C2 | semidirect |
| 5. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761364 | C2 | semidirect |
| 7. Q8×Q16×C79 | C2 | semidirect |
| 68. Q16×C79 | SD16 | semidirect |
| 90. Q8×C79 | SD32 | semidirect |
| 128. Q8×Q16 | D79 | semidirect |
| 135. C79 | #12354 | semidirect |
| 189. Q16 | #11929611 | semidirect |
| 218. Q8 | #14579104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765625 | 2 |
| #23765440 | 2 |
| #23762760 | 2 |
| #23761458 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761364 | 2 |
| Q8×Q16×C79 | 2 |
| #12354 | 79 |