Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22590142 | C2 | semidirect |
| 3. #22587102 | C2 | semidirect |
| 4. #22586387 | C2 | semidirect |
| 5. #22586386 | C2 | semidirect |
| 6. #22586385 | C2 | semidirect |
| 7. C71×#1361 | C2 | semidirect |
| 17. C4⋊(C71⋊C16) | C22 | semidirect |
| 20. #17985752 | C22 | semidirect |
| 23. C4⋊C16×C71 | C22 | semidirect |
| 24. #335×C71 | C22 | semidirect |
| 165. #1361 | D71 | semidirect |
| 166. C71 | #11964 | semidirect |
| 178. C4⋊C16 | C2×D71 | semidirect |
| 182. #335 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D71 | 2 |
| #22590142 | 2 |
| #22587102 | 2 |
| #22586387 | 2 |
| #22586386 | 2 |
| #22586385 | 2 |
| C71×#1361 | 2 |
| #11964 | 71 |