Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22589168 | C2 | semidirect |
| 3. #22587099 | C2 | semidirect |
| 4. #22586792 | C2 | semidirect |
| 5. C71×#1744 | C2 | semidirect |
| 7. #17986404 | C4 | semidirect |
| 8. #17986376 | C4 | semidirect |
| 9. #17986346 | C4 | semidirect |
| 73. C42×C71 | D8 | semidirect |
| 129. #1744 | D71 | semidirect |
| 132. C71 | #9847 | semidirect |
| 200. C42 | D568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| #22589168 | 2 |
| #22587099 | 2 |
| #22586792 | 2 |
| C71×#1744 | 2 |
| #9847 | 71 |