Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22591633 | C2 | semidirect |
| 3. #22586241 | C2 | semidirect |
| 4. #22586169 | C2 | semidirect |
| 36. C4⋊Q8×C71 | Q8 | semidirect |
| 37. #127×C71 | Q8 | semidirect |
| 146. C71 | #10370 | semidirect |
| 163. C4⋊Q8 | Dic142 | semidirect |
| 164. #127 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591633 | 2 |
| #22586835 | 2 |
| #22586241 | 2 |
| #22586169 | 2 |
| C71×#1963 | 2 |
| #10370 | 71 |