Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 5. #22586439 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C2×#365×C71 | C2 | semidirect |
| 18. (C2×D71)⋊C16 | C4 | semidirect |
| 40. C2×C71⋊C16 | C2×C4 | semidirect |
| 52. C2×C16×C71 | C2×C4 | semidirect |
| 134. C2×D71 | #365 | semidirect |
| 150. C2×#365 | D71 | semidirect |
| 155. C71 | #12929 | semidirect |
| 194. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×D71 | 2 |
| C2×#17985823 | 2 |
| #22589950 | 2 |
| #22588375 | 2 |
| #22586439 | 2 |
| #22586438 | 2 |
| C2×#365×C71 | 2 |
| #12929 | 71 |