Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#17985777 | C2 | semidirect |
| 3. #22586374 | C2 | semidirect |
| 4. #22586372 | C2 | semidirect |
| 5. C2×#347×C71 | C2 | semidirect |
| 141. C2×#347 | D71 | semidirect |
| 144. C71 | #11911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598686 | 2 |
| C2×#17985777 | 2 |
| #22586374 | 2 |
| #22586372 | 2 |
| C2×#347×C71 | 2 |
| #11911 | 71 |