Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
286 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #22586533 | C2 | direct (N × H) |
| 97. C2×C71 | #1420 | semidirect |
| 103. C71 | C2×#1420 | semidirect |
| 195. C2 | #22586533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985833 | 2 |
| C2×#17985829 | 2 |
| #22586533 | 2 |
| C22×Q32×C71 | 2 |
| C2×#1420 | 71 |