Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#17986378 | C2 | semidirect |
| 3. C2×#17986290 | C2 | semidirect |
| 4. #22587486 | C2 | direct (N × H) |
| 5. C2×#17985726 | C2 | semidirect |
| 6. C2×#333×C71 | C2 | semidirect |
| 17. #17986378 | C22 | semidirect |
| 19. #17986290 | C22 | semidirect |
| 23. #17985726 | C22 | semidirect |
| 26. #333×C71 | C22 | semidirect |
| 152. C2×C71 | #1634 | semidirect |
| 160. C2×#333 | D71 | semidirect |
| 162. C71 | C2×#1634 | semidirect |
| 181. #333 | C2×D71 | semidirect |
| 308. C2 | #22587486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986715 | 2 |
| C2×#17986378 | 2 |
| C2×#17986290 | 2 |
| #22587486 | 2 |
| C2×#17985726 | 2 |
| C2×#333×C71 | 2 |
| C2×#1634 | 71 |