Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
468 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 75 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×#17985796 | C2 | semidirect |
| 3. #22586496 | C2 | direct (N × H) |
| 4. C2×#354×C71 | C2 | semidirect |
| 7. C2×#14556125 | C4 | semidirect |
| 10. #17986389 | C4 | semidirect |
| 13. C2×#14556039 | C4 | semidirect |
| 15. #17985796 | C22 | semidirect |
| 19. #354×C71 | C22 | semidirect |
| 34. #14556125 | C2×C4 | semidirect |
| 38. #14556039 | C2×C4 | semidirect |
| 158. C2×C71 | #1406 | semidirect |
| 163. C2×#354 | D71 | semidirect |
| 165. C71 | C2×#1406 | semidirect |
| 180. #354 | C2×D71 | semidirect |
| 319. C2 | #22586496 | 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×#17985796 | 2 |
| #22586496 | 2 |
| C2×#354×C71 | 2 |
| C2×#1406 | 71 |