Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
288 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 88. Q8×C79 | Q32 | semidirect |
| 128. C79 | #12358 | semidirect |
| 211. Q8 | #14579107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765629 | 2 |
| #23765450 | 2 |
| #23762770 | 2 |
| #23761458 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761364 | 2 |
| Q8×Q16×C79 | 2 |
| #12358 | 79 |