Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
736 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22589309 | C2 | semidirect |
| 4. C2×#17985740 | C2 | semidirect |
| 8. #17986749 | C4 | semidirect |
| 172. C71 | #8507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986749 | 2 |
| #22589309 | 2 |
| #22589157 | 2 |
| C2×#17985740 | 2 |
| C2×#329×C71 | 2 |
| #8507 | 71 |