Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 21. C2×C71⋊C16 | Q8 | semidirect |
| 24. #14556060 | Q8 | semidirect |
| 100. C71 | #13459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590112 | 2 |
| #22589093 | 2 |
| #22586441 | 2 |
| #22586420 | 2 |
| C71×#3162 | 2 |
| #13459 | 71 |