Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590178 | C2 | semidirect |
| 3. #22586415 | C2 | semidirect |
| 4. #22586313 | C2 | semidirect |
| 5. #22586312 | C2 | semidirect |
| 6. #22586256 | C2 | semidirect |
| 7. C71×#2170 | C2 | semidirect |
| 25. #14556074 | C8 | semidirect |
| 26. #14556072 | C8 | semidirect |
| 27. #14556071 | C8 | semidirect |
| 28. #14556069 | C8 | semidirect |
| 105. #2170 | D71 | semidirect |
| 110. C71 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590219 | 2 |
| #22590178 | 2 |
| #22586415 | 2 |
| #22586313 | 2 |
| #22586312 | 2 |
| #22586256 | 2 |
| C71×#2170 | 2 |
| #12047 | 71 |