Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 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. #22589258 | C2 | semidirect |
| 3. #22586938 | C2 | semidirect |
| 4. #22586886 | C2 | semidirect |
| 5. #22586204 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#2337 | C2 | semidirect |
| 9. #17986389 | C4 | semidirect |
| 10. #17986358 | C4 | semidirect |
| 35. #14556128 | C2×C4 | semidirect |
| 36. #14556125 | C2×C4 | semidirect |
| 52. #14556039 | C2×C4 | semidirect |
| 223. #2337 | D71 | semidirect |
| 229. C71 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599327 | 2 |
| #22589258 | 2 |
| #22586938 | 2 |
| #22586886 | 2 |
| #22586204 | 2 |
| #22586196 | 2 |
| C71×#2337 | 2 |
| #9381 | 71 |