Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
484 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22596612 | C2 | semidirect |
| 3. #22586222 | C2 | semidirect |
| 4. #22586221 | C2 | semidirect |
| 39. #127×C71 | Q8 | semidirect |
| 148. C71 | #10358 | semidirect |
| 169. #127 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596612 | 2 |
| #22589165 | 2 |
| #22586222 | 2 |
| #22586221 | 2 |
| C71×#1961 | 2 |
| #10358 | 71 |