Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #22589314 | C2 | semidirect |
| 5. #22586222 | C2 | semidirect |
| 6. #22586221 | C2 | semidirect |
| 7. C71×#1960 | C2 | semidirect |
| 10. #17986361 | C4 | semidirect |
| 53. #14556039 | C2×C4 | semidirect |
| 63. C4⋊Q8×C71 | C2×C4 | semidirect |
| 220. #1960 | D71 | semidirect |
| 224. C71 | #8999 | semidirect |
| 257. C4⋊Q8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986361 | 2 |
| #22591511 | 2 |
| #22589314 | 2 |
| C2×#17985738 | 2 |
| #22586222 | 2 |
| #22586221 | 2 |
| C71×#1960 | 2 |
| #8999 | 71 |