Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22590011 | C2 | semidirect |
| 3. #22589990 | C2 | semidirect |
| 4. #22589989 | C2 | semidirect |
| 5. #22588384 | C2 | semidirect |
| 6. #22588142 | C2 | semidirect |
| 7. C71×#2128 | C2 | semidirect |
| 8. C22×#11765850 | C4 | semidirect |
| 16. #17986035 | C4 | semidirect |
| 17. #17986004 | C4 | semidirect |
| 18. #17986003 | C4 | semidirect |
| 222. #2128 | D71 | semidirect |
| 227. C71 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597985 | 2 |
| #22590011 | 2 |
| #22589990 | 2 |
| #22589989 | 2 |
| #22588384 | 2 |
| #22588142 | 2 |
| C71×#2128 | 2 |
| #13231 | 71 |