Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
346 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #22590290 | C2 | semidirect |
| 3. #22589627 | C2 | semidirect |
| 4. #22586334 | C2 | semidirect |
| 5. #22586331 | C2 | semidirect |
| 6. #22586291 | C2 | semidirect |
| 7. C71×#3256 | C2 | semidirect |
| 171. #3256 | D71 | semidirect |
| 178. C71 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590290 | 2 |
| #22590285 | 2 |
| #22589627 | 2 |
| #22586334 | 2 |
| #22586331 | 2 |
| #22586291 | 2 |
| C71×#3256 | 2 |
| #12175 | 71 |