Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 406 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. #22598863 | C2 | semidirect |
| 5. #22586447 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 29. C2×D568 | Q8 | semidirect |
| 154. #1386 | D71 | semidirect |
| 156. C71 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598863 | 2 |
| #22590057 | 2 |
| #22590055 | 2 |
| #22589214 | 2 |
| #22586447 | 2 |
| #22586423 | 2 |
| C71×#1386 | 2 |
| #13367 | 71 |