Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
772 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 772 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. #22597388 | C2 | semidirect |
| 3. #22588270 | C2 | semidirect |
| 4. #22588260 | C2 | semidirect |
| 5. #22586246 | C2 | semidirect |
| 6. #22586216 | C2 | semidirect |
| 7. C71×#1513 | C2 | semidirect |
| 11. #17986149 | C4 | semidirect |
| 13. #17986132 | C4 | semidirect |
| 279. #1513 | D71 | semidirect |
| 282. C71 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597566 | 2 |
| #22597388 | 2 |
| #22588270 | 2 |
| #22588260 | 2 |
| #22586246 | 2 |
| #22586216 | 2 |
| C71×#1513 | 2 |
| #9520 | 71 |