Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 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. #22591516 | C2 | semidirect |
| 3. #22587053 | C2 | semidirect |
| 4. #22586887 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586204 | C2 | semidirect |
| 7. C71×#1514 | C2 | semidirect |
| 11. #17986375 | C4 | semidirect |
| 12. #17986373 | C4 | semidirect |
| 45. C4×C71⋊C8 | C2×C4 | semidirect |
| 50. C4⋊Q8×C71 | C2×C4 | semidirect |
| 51. #127×C71 | C2×C4 | semidirect |
| 186. #1514 | D71 | semidirect |
| 189. C71 | #9428 | semidirect |
| 217. C4⋊Q8 | C4×D71 | semidirect |
| 222. #127 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598793 | 2 |
| #22591516 | 2 |
| #22587053 | 2 |
| #22586887 | 2 |
| #22586206 | 2 |
| #22586204 | 2 |
| C71×#1514 | 2 |
| #9428 | 71 |