Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×#17985827 | C2 | semidirect |
| 3. #22586528 | C2 | direct (N × H) |
| 4. C2×M64×C71 | C2 | semidirect |
| 8. #17986431 | C4 | semidirect |
| 10. C2×Dic568 | C4 | semidirect |
| 12. C2×D1136 | C4 | semidirect |
| 15. #17985827 | C22 | semidirect |
| 18. M64×C71 | C22 | semidirect |
| 30. Dic568 | C2×C4 | semidirect |
| 34. D1136 | C2×C4 | semidirect |
| 111. C2×C71 | #1418 | semidirect |
| 115. C2×M64 | D71 | semidirect |
| 118. C71 | C2×#1418 | semidirect |
| 130. M64 | C2×D71 | semidirect |
| 225. C2 | #22586528 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986431 | 2 |
| C2×#17985827 | 2 |
| #22586528 | 2 |
| C2×M64×C71 | 2 |
| C2×#1418 | 71 |