Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588545 | C2 | semidirect |
| 3. #22588523 | C2 | semidirect |
| 5. #22586226 | C2 | semidirect |
| 6. #22586188 | C2 | semidirect |
| 22. #17985736 | C4 | semidirect |
| 23. #17985736 | C4 | semidirect |
| 24. #17985733 | C4 | semidirect |
| 25. #17985733 | C4 | semidirect |
| 225. C71 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597388 | 2 |
| #22588545 | 2 |
| #22588523 | 2 |
| #22586831 | 2 |
| #22586226 | 2 |
| #22586188 | 2 |
| C71×#1871 | 2 |
| #8874 | 71 |