Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #22586404 | C2 | semidirect |
| 5. #22586395 | C2 | semidirect |
| 6. #22586389 | C2 | semidirect |
| 7. C71×#1707 | C2 | semidirect |
| 111. #1707 | D71 | semidirect |
| 116. C71 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590474 | 2 |
| #22590382 | 2 |
| C8×D568 | 2 |
| #22586404 | 2 |
| #22586395 | 2 |
| #22586389 | 2 |
| C71×#1707 | 2 |
| #12422 | 71 |