Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 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. #22590031 | C2 | semidirect |
| 3. #22589989 | C2 | semidirect |
| 4. #22588390 | C2 | semidirect |
| 5. C71×#1757 | C2 | semidirect |
| 6. C22×D568 | C4 | semidirect |
| 13. #17986037 | C4 | semidirect |
| 14. #17986005 | C4 | semidirect |
| 171. #1757 | D71 | semidirect |
| 172. C71 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597988 | 2 |
| #22590031 | 2 |
| #22589989 | 2 |
| #22588390 | 2 |
| C71×#1757 | 2 |
| #13234 | 71 |