Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#17985821 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985776 | C2 | semidirect |
| 5. #22589234 | C2 | semidirect |
| 6. #22589214 | C2 | semidirect |
| 7. C2×#360×C71 | C2 | semidirect |
| 11. C2×#14556071 | C4 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 86. C71⋊C16 | C22⋊C4 | semidirect |
| 176. C2×#360 | D71 | semidirect |
| 180. C71 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C2×#17985821 | 2 |
| C2×#17985813 | 2 |
| C2×#17985776 | 2 |
| #22589234 | 2 |
| #22589214 | 2 |
| C2×#360×C71 | 2 |
| #13249 | 71 |