Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22590114 | C2 | semidirect |
| 5. #22588227 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#1385 | C2 | semidirect |
| 16. #17985814 | C4 | semidirect |
| 17. #17985811 | C4 | semidirect |
| 144. #1385 | D71 | semidirect |
| 146. C71 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590114 | 2 |
| #22590087 | 2 |
| #22590077 | 2 |
| #22589231 | 2 |
| #22588227 | 2 |
| #22586423 | 2 |
| C71×#1385 | 2 |
| #13140 | 71 |