Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 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×#17985823 | C2 | semidirect |
| 4. #22589128 | C2 | semidirect |
| 5. #22586439 | C2 | semidirect |
| 6. #22586427 | C2 | semidirect |
| 19. #17985806 | C4 | semidirect |
| 37. C2×C71⋊C16 | C2×C4 | semidirect |
| 39. #14556064 | C2×C4 | semidirect |
| 159. C71 | #12949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597224 | 2 |
| C2×#17985823 | 2 |
| #22590068 | 2 |
| #22589128 | 2 |
| #22586439 | 2 |
| #22586427 | 2 |
| C71×#2148 | 2 |
| #12949 | 71 |