Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#17985816 | C2 | semidirect |
| 4. C2×#17985814 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 169. #1389 | D71 | semidirect |
| 170. C71 | #13078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22597996 | 2 |
| C2×#17985816 | 2 |
| C2×#17985814 | 2 |
| #22588387 | 2 |
| #22586456 | 2 |
| C71×#1389 | 2 |
| #13078 | 71 |