Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597257 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22589236 | C2 | semidirect |
| 5. #22586435 | C2 | semidirect |
| 6. #22586430 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 12. C2×#14556074 | C4 | semidirect |
| 13. C2×#14556072 | C4 | semidirect |
| 14. C2×#14556071 | C4 | semidirect |
| 15. C2×#14556069 | C4 | semidirect |
| 185. #2145 | D71 | semidirect |
| 190. C71 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986429 | 2 |
| #22597257 | 2 |
| #22590069 | 2 |
| #22589236 | 2 |
| #22586435 | 2 |
| #22586430 | 2 |
| C71×#2145 | 2 |
| #13016 | 71 |