Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22590554 | C2 | direct (N × H) |
| 3. C2×#17985823 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. C2×#17985781 | C2 | semidirect |
| 6. C2×#430×C71 | C2 | semidirect |
| 14. #17985823 | C22 | semidirect |
| 15. #17985811 | C22 | semidirect |
| 16. #17985781 | C22 | semidirect |
| 20. #430×C71 | C22 | semidirect |
| 150. C2×C71 | #2238 | semidirect |
| 154. C2×#430 | D71 | semidirect |
| 159. C71 | C2×#2238 | semidirect |
| 168. #430 | C2×D71 | semidirect |
| 303. C2 | #22590554 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986252 | 2 |
| #22590554 | 2 |
| C2×#17985823 | 2 |
| C2×#17985811 | 2 |
| C2×#17985781 | 2 |
| C2×#430×C71 | 2 |
| C2×#2238 | 71 |