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. #22590113 | C2 | semidirect |
| 3. C2×#17985821 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 21. #17985784 | C4 | semidirect |
| 43. C2×C71⋊C16 | C2×C4 | semidirect |
| 56. M32×C71 | C2×C4 | semidirect |
| 158. #1386 | D71 | semidirect |
| 160. C71 | #12934 | semidirect |
| 200. M32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596931 | 2 |
| #22590113 | 2 |
| C2×#17985821 | 2 |
| #22589969 | 2 |
| #22588391 | 2 |
| #22586441 | 2 |
| C71×#1386 | 2 |
| #12934 | 71 |