Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22590614 | C2 | semidirect |
| 3. #22586539 | C2 | semidirect |
| 4. Dic71⋊C32 | C2 | semidirect |
| 7. C71×#1423 | C2 | semidirect |
| 23. D1136 | Q8 | semidirect |
| 83. #1423 | D71 | semidirect |
| 87. C71 | #13703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590614 | 2 |
| #22590186 | 2 |
| #22586539 | 2 |
| Dic71⋊C32 | 2 |
| #22586519 | 2 |
| #22586517 | 2 |
| C71×#1423 | 2 |
| #13703 | 71 |