Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22601442 | C2 | semidirect |
| 3. #22590076 | C2 | semidirect |
| 4. #22588383 | C2 | semidirect |
| 5. #22586446 | C2 | semidirect |
| 6. #22586445 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 14. #17986254 | C4 | semidirect |
| 15. #17986249 | C4 | semidirect |
| 43. #14556068 | D4 | semidirect |
| 65. M32×C71 | D4 | semidirect |
| 185. #2145 | D71 | semidirect |
| 189. C71 | #13077 | semidirect |
| 238. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22597998 | 2 |
| #22590076 | 2 |
| #22588383 | 2 |
| #22586446 | 2 |
| #22586445 | 2 |
| C71×#2145 | 2 |
| #13077 | 71 |