Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 46. Dic568 | Q8 | semidirect |
| 134. C71 | #33957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601228 | 2 |
| #22590625 | 2 |
| #22590503 | 2 |
| #22590501 | 2 |
| #22590491 | 2 |
| #22590248 | 2 |
| #22590210 | 2 |
| C4×Dic568 | 2 |
| C71×#2253 | 2 |
| #33957 | 71 |