Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22589330 | C2 | semidirect |
| 5. #22586250 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1558 | C2 | semidirect |
| 185. #1558 | D71 | semidirect |
| 189. C71 | #9337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599367 | 2 |
| #22597512 | 2 |
| #22589330 | 2 |
| #22586948 | 2 |
| #22586250 | 2 |
| #22586211 | 2 |
| C71×#1558 | 2 |
| #9337 | 71 |