Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22589259 | C2 | semidirect |
| 3. C4×#14556060 | C2 | semidirect |
| 4. #22586836 | C2 | semidirect |
| 5. C71×#1451 | C2 | semidirect |
| 7. #17986404 | C4 | semidirect |
| 8. #17986376 | C4 | semidirect |
| 9. #17986346 | C4 | semidirect |
| 119. C8×C71 | #104 | semidirect |
| 146. #1451 | D71 | semidirect |
| 147. C71 | #9721 | semidirect |
| 261. C8 | #14556054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| #22589259 | 2 |
| C4×#14556060 | 2 |
| #22586836 | 2 |
| C71×#1451 | 2 |
| #9721 | 71 |