Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #17986399 | C4 | semidirect |
| 127. C71 | #13273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986399 | 2 |
| C2×#17985819 | 2 |
| #22588222 | 2 |
| #22586447 | 2 |
| #22586446 | 2 |
| #22586440 | 2 |
| C71×#1383 | 2 |
| #13273 | 71 |