Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 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 |
|---|---|---|
| 3. #22588275 | C2 | semidirect |
| 5. #22586245 | C2 | semidirect |
| 6. #22586216 | C2 | semidirect |
| 7. C71×#1784 | C2 | semidirect |
| 11. #17986155 | C4 | semidirect |
| 13. #17986138 | C4 | semidirect |
| 254. #1784 | D71 | semidirect |
| 258. C71 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597574 | 2 |
| #22597390 | 2 |
| #22588275 | 2 |
| #22586884 | 2 |
| #22586245 | 2 |
| #22586216 | 2 |
| C71×#1784 | 2 |
| #9519 | 71 |