Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 1. C2×#17986442 | C2 | semidirect |
| 3. C2×#17986274 | C2 | semidirect |
| 4. C2×#17985816 | C2 | semidirect |
| 5. #22590069 | C2 | semidirect |
| 6. #22586452 | C2 | semidirect |
| 7. C71×#2115 | C2 | semidirect |
| 210. #2115 | D71 | semidirect |
| 212. C71 | #13324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986442 | 2 |
| #22598060 | 2 |
| C2×#17986274 | 2 |
| C2×#17985816 | 2 |
| #22590069 | 2 |
| #22586452 | 2 |
| C71×#2115 | 2 |
| #13324 | 71 |