Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 3. #22588386 | C2 | semidirect |
| 4. #22586470 | C2 | semidirect |
| 5. C71×#1813 | C2 | semidirect |
| 6. C22×C8×D71 | C4 | semidirect |
| 13. #17986027 | C4 | semidirect |
| 16. #17985962 | C4 | semidirect |
| 17. #17985954 | C4 | semidirect |
| 189. #1813 | D71 | semidirect |
| 192. C71 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597032 | 2 |
| #22589982 | 2 |
| #22588386 | 2 |
| #22586470 | 2 |
| C71×#1813 | 2 |
| #12805 | 71 |