Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22590563 | C2 | semidirect |
| 3. #22590488 | C2 | semidirect |
| 4. #22587740 | C2 | semidirect |
| 5. #22586300 | C2 | semidirect |
| 6. #22586294 | C2 | semidirect |
| 7. C71×#1361 | C2 | semidirect |
| 10. #17986404 | C22 | semidirect |
| 20. C4×C71⋊C16 | C22 | semidirect |
| 23. C4⋊C16×C71 | C22 | semidirect |
| 24. #335×C71 | C22 | semidirect |
| 154. #1361 | D71 | semidirect |
| 157. C71 | #12372 | semidirect |
| 169. C4⋊C16 | C2×D71 | semidirect |
| 173. #335 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600015 | 2 |
| #22590563 | 2 |
| #22590488 | 2 |
| #22587740 | 2 |
| #22586300 | 2 |
| #22586294 | 2 |
| C71×#1361 | 2 |
| #12372 | 71 |