Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
878 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. #22590077 | C2 | semidirect |
| 3. #22590061 | C2 | semidirect |
| 4. #22588386 | C2 | semidirect |
| 5. C71×#2115 | C2 | semidirect |
| 11. C2×#14556150 | C4 | semidirect |
| 13. C22×Dic284 | C4 | semidirect |
| 172. #2115 | D71 | semidirect |
| 174. C71 | #12742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986816 | 2 |
| #22590077 | 2 |
| #22590061 | 2 |
| #22588386 | 2 |
| C71×#2115 | 2 |
| #12742 | 71 |