Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22594459 | C2 | semidirect |
| 4. #22587056 | C2 | semidirect |
| 5. #22586941 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 180. #1300 | D71 | semidirect |
| 181. C71 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599532 | 2 |
| #22598734 | 2 |
| #22594459 | 2 |
| #22587056 | 2 |
| #22586941 | 2 |
| #22586847 | 2 |
| C71×#1300 | 2 |
| #10093 | 71 |