Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1010 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 187 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. C2×#17986365 | C2 | semidirect |
| 3. #22587638 | C2 | direct (N × H) |
| 4. C2×#17985741 | C2 | semidirect |
| 5. C2×#17985739 | C2 | semidirect |
| 6. C2×#563×C71 | C2 | semidirect |
| 13. #17986365 | C22 | semidirect |
| 18. #17985741 | C22 | semidirect |
| 19. #17985739 | C22 | semidirect |
| 22. #563×C71 | C22 | semidirect |
| 172. C2×C71 | #1657 | semidirect |
| 176. C2×#563 | D71 | semidirect |
| 182. C71 | C2×#1657 | semidirect |
| 187. #563 | C2×D71 | semidirect |
| 348. C2 | #22587638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986389 | 2 |
| C2×#17986365 | 2 |
| #22587638 | 2 |
| C2×#17985741 | 2 |
| C2×#17985739 | 2 |
| C2×#563×C71 | 2 |
| C2×#1657 | 71 |