Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22589260 | C2 | semidirect |
| 3. #22589258 | C2 | semidirect |
| 4. C4×#14556059 | C2 | semidirect |
| 5. #22586836 | C2 | semidirect |
| 6. #22586630 | C2 | semidirect |
| 7. C71×#1502 | C2 | semidirect |
| 9. #17986402 | C4 | semidirect |
| 10. #17986375 | C4 | semidirect |
| 11. #17986347 | C4 | semidirect |
| 12. #17986345 | C4 | semidirect |
| 171. C71⋊C8 | #104 | semidirect |
| 207. #1502 | D71 | semidirect |
| 209. C71 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598915 | 2 |
| #22589260 | 2 |
| #22589258 | 2 |
| C4×#14556059 | 2 |
| #22586836 | 2 |
| #22586630 | 2 |
| C71×#1502 | 2 |
| #9721 | 71 |