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×#17985823 | C2 | semidirect |
| 3. C2×#17985811 | C2 | semidirect |
| 4. C2×#17985809 | C2 | semidirect |
| 5. C2×#17985777 | C2 | semidirect |
| 6. #22589216 | C2 | semidirect |
| 7. C71×#1975 | C2 | semidirect |
| 11. C2×#14556071 | C4 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 81. C71⋊C16 | C22⋊C4 | semidirect |
| 178. #1975 | 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×#17985823 | 2 |
| C2×#17985811 | 2 |
| C2×#17985809 | 2 |
| C2×#17985777 | 2 |
| #22589216 | 2 |
| C71×#1975 | 2 |
| #13249 | 71 |