Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22591153 | C2 | semidirect |
| 3. #22586937 | C2 | semidirect |
| 4. #22586887 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1980 | C2 | semidirect |
| 9. #17986386 | C4 | semidirect |
| 10. #17986361 | C4 | semidirect |
| 54. #14556039 | C2×C4 | semidirect |
| 63. C4⋊Q8×C71 | C2×C4 | semidirect |
| 64. #127×C71 | C2×C4 | semidirect |
| 224. #1980 | D71 | semidirect |
| 229. C71 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D71 | semidirect |
| 261. #127 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599323 | 2 |
| #22591153 | 2 |
| #22586937 | 2 |
| #22586887 | 2 |
| #22586205 | 2 |
| #22586196 | 2 |
| C71×#1980 | 2 |
| #9381 | 71 |