Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22588475 | C2 | semidirect |
| 4. C2×#17985741 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 7. C71×#1992 | C2 | semidirect |
| 208. #1992 | D71 | semidirect |
| 214. C71 | #10426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596390 | 2 |
| #22589154 | 2 |
| #22588475 | 2 |
| C2×#17985741 | 2 |
| C2×#17985738 | 2 |
| #22586222 | 2 |
| C71×#1992 | 2 |
| #10426 | 71 |