Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22597394 | C2 | semidirect |
| 3. #22586845 | C2 | semidirect |
| 4. C2×#17985734 | C2 | semidirect |
| 5. #22586701 | C2 | semidirect |
| 6. #22586182 | C2 | semidirect |
| 7. C71×#1298 | C2 | semidirect |
| 10. #17986335 | C4 | semidirect |
| 12. #17986318 | C4 | semidirect |
| 15. #17986152 | C4 | semidirect |
| 17. #17986135 | C4 | semidirect |
| 251. #1298 | D71 | semidirect |
| 253. C71 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599107 | 2 |
| #22597394 | 2 |
| #22586845 | 2 |
| C2×#17985734 | 2 |
| #22586701 | 2 |
| #22586182 | 2 |
| C71×#1298 | 2 |
| #9264 | 71 |