Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #22589302 | C2 | semidirect |
| 3. #22588497 | C2 | semidirect |
| 4. C2×C8×C71⋊C8 | C2 | semidirect |
| 16. #492×C71 | C4 | semidirect |
| 46. C2×C71⋊C8 | SD16 | semidirect |
| 101. C8×C71 | #102 | semidirect |
| 131. C71 | #9820 | semidirect |
| 136. #492 | Dic71 | semidirect |
| 228. C8 | #14556049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589302 | 2 |
| #22589147 | 2 |
| #22588497 | 2 |
| C2×C8×C71⋊C8 | 2 |
| C2×#492×C71 | 2 |
| #9820 | 71 |