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. #22590077 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22588383 | C2 | semidirect |
| 6. #22586447 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 15. #17986258 | C4 | semidirect |
| 16. #17986253 | C4 | semidirect |
| 50. #14556068 | D4 | semidirect |
| 63. M32×C71 | D4 | semidirect |
| 188. #1386 | D71 | semidirect |
| 189. C71 | #13077 | semidirect |
| 238. M32 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22598003 | 2 |
| #22590077 | 2 |
| #22590075 | 2 |
| #22588383 | 2 |
| #22586447 | 2 |
| C71×#1386 | 2 |
| #13077 | 71 |