Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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×#17985826 | C2 | semidirect |
| 5. #22586450 | C2 | semidirect |
| 6. #22586429 | C2 | semidirect |
| 7. C71×#1952 | C2 | semidirect |
| 18. #17985805 | C4 | semidirect |
| 45. C2×C71⋊C16 | C2×C4 | semidirect |
| 56. #108×C71 | C2×C4 | semidirect |
| 164. #1952 | D71 | semidirect |
| 167. C71 | #12946 | semidirect |
| 212. #108 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597217 | 2 |
| C2×#17985826 | 2 |
| C2×#17985805 | 2 |
| #22590050 | 2 |
| #22586450 | 2 |
| #22586429 | 2 |
| C71×#1952 | 2 |
| #12946 | 71 |