Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 1. #22589135 | C2 | semidirect |
| 2. #22588332 | C2 | semidirect |
| 3. #22587017 | C2 | semidirect |
| 4. #22586791 | C2 | semidirect |
| 6. #17986023 | C22 | semidirect |
| 7. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 10. C2×C4×C71⋊C8 | C22 | semidirect |
| 197. C71 | #8353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589135 | 2 |
| #22588332 | 2 |
| #22587017 | 2 |
| #22586791 | 2 |
| C71×#3496 | 2 |
| #8353 | 71 |