Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588376 | C2 | semidirect |
| 3. #22588118 | C2 | semidirect |
| 4. #22586855 | C2 | semidirect |
| 5. #22586701 | C2 | semidirect |
| 6. #22586700 | C2 | semidirect |
| 7. C71×#1507 | C2 | semidirect |
| 8. C22×#11765850 | C4 | semidirect |
| 16. C2×#14556061 | C4 | semidirect |
| 17. C2×#14556049 | C4 | semidirect |
| 18. C2×#14556048 | C4 | semidirect |
| 229. #1507 | D71 | semidirect |
| 232. C71 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986233 | 2 |
| #22588376 | 2 |
| #22588118 | 2 |
| #22586855 | 2 |
| #22586701 | 2 |
| #22586700 | 2 |
| C71×#1507 | 2 |
| #9818 | 71 |