Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
658 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 95 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×#17986364 | C2 | semidirect |
| 3. #22596391 | C2 | semidirect |
| 4. #22589164 | C2 | semidirect |
| 5. C2×#17985740 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 7. C2×#329×C71 | C2 | semidirect |
| 216. C2×#329 | D71 | semidirect |
| 218. C71 | #10079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986389 | 2 |
| C2×#17986364 | 2 |
| #22596391 | 2 |
| #22589164 | 2 |
| C2×#17985740 | 2 |
| #22586222 | 2 |
| C2×#329×C71 | 2 |
| #10079 | 71 |