Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22591311 | C2 | semidirect |
| 3. #22586901 | C2 | semidirect |
| 4. #22586834 | C2 | semidirect |
| 5. #22586732 | C2 | semidirect |
| 6. #22586200 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 12. #17986205 | C4 | semidirect |
| 13. #17986195 | C4 | semidirect |
| 215. #1303 | D71 | semidirect |
| 217. C71 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597806 | 2 |
| #22591311 | 2 |
| #22586901 | 2 |
| #22586834 | 2 |
| #22586732 | 2 |
| #22586200 | 2 |
| C71×#1303 | 2 |
| #9181 | 71 |