Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22586379 | C2 | direct (N × H) |
| 84. C2×C71 | #1358 | semidirect |
| 89. C71 | C2×#1358 | semidirect |
| 169. C2 | #22586379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985820 | 2 |
| #22586379 | 2 |
| C2×#494×C71 | 2 |
| C2×#1358 | 71 |