Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590579 | C2 | semidirect |
| 3. #22590484 | C2 | semidirect |
| 4. #22586382 | C2 | semidirect |
| 5. #22586306 | C2 | semidirect |
| 6. #22586298 | C2 | semidirect |
| 7. C71×#1693 | C2 | semidirect |
| 17. C4⋊(C71⋊C16) | C22 | semidirect |
| 21. #17985775 | C22 | semidirect |
| 22. #500×C71 | C22 | semidirect |
| 25. #334×C71 | C22 | semidirect |
| 82. D568 | SD16 | semidirect |
| 170. #1693 | D71 | semidirect |
| 174. C71 | #12378 | semidirect |
| 177. #500 | C2×D71 | semidirect |
| 192. #334 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599952 | 2 |
| #22590579 | 2 |
| #22590484 | 2 |
| #22586382 | 2 |
| #22586306 | 2 |
| #22586298 | 2 |
| C71×#1693 | 2 |
| #12378 | 71 |