Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×C4×C71⋊C16 | C2 | semidirect |
| 4. #22589088 | C2 | semidirect |
| 5. #22586437 | C2 | semidirect |
| 6. #22586433 | C2 | semidirect |
| 14. #17985803 | C4 | semidirect |
| 15. #17985800 | C4 | semidirect |
| 145. C71 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985806 | 2 |
| #22590047 | 2 |
| C2×C4×C71⋊C16 | 2 |
| #22589088 | 2 |
| #22586437 | 2 |
| #22586433 | 2 |
| C71×#1974 | 2 |
| #13151 | 71 |