Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 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. #22590061 | C2 | semidirect |
| 4. #22590059 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 7. C71×#1384 | C2 | semidirect |
| 15. #17986258 | C4 | semidirect |
| 170. #1384 | D71 | semidirect |
| 171. C71 | #13075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22597996 | 2 |
| #22590061 | 2 |
| #22590059 | 2 |
| #22588383 | 2 |
| #22586441 | 2 |
| C71×#1384 | 2 |
| #13075 | 71 |