Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590615 | C2 | semidirect |
| 2. #22586539 | C2 | semidirect |
| 3. C4⋊(C71⋊C32) | C2 | semidirect |
| 22. D16×C71 | Q8 | semidirect |
| 76. C71 | #13703 | semidirect |
| 90. D16 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590615 | 2 |
| #22586539 | 2 |
| C4⋊(C71⋊C32) | 2 |
| #22586518 | 2 |
| C4×D16×C71 | 2 |
| #13703 | 71 |