Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22597411 | C2 | semidirect |
| 3. #22588306 | C2 | semidirect |
| 4. #22586468 | C2 | semidirect |
| 5. C71×#2126 | C2 | semidirect |
| 8. #17986181 | C4 | semidirect |
| 10. #17986171 | C4 | semidirect |
| 197. #2126 | D71 | semidirect |
| 200. C71 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597688 | 2 |
| #22597411 | 2 |
| #22588306 | 2 |
| #22586468 | 2 |
| C71×#2126 | 2 |
| #13053 | 71 |