Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22593983 | C2 | semidirect |
| 4. #22586234 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 51. C4⋊Q8×C71 | Q8 | semidirect |
| 52. #127×C71 | Q8 | semidirect |
| 189. C71 | #10378 | semidirect |
| 212. C4⋊Q8 | Dic142 | semidirect |
| 213. #127 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22593983 | 2 |
| #22586887 | 2 |
| #22586848 | 2 |
| #22586234 | 2 |
| #22586205 | 2 |
| #22586196 | 2 |
| C71×#1980 | 2 |
| #10378 | 71 |