Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 426 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. #22587096 | C2 | semidirect |
| 3. #22586308 | C2 | semidirect |
| 4. C71×#2163 | C2 | semidirect |
| 15. #17985750 | C22 | semidirect |
| 19. #346×C71 | C22 | semidirect |
| 57. D568 | M16 | semidirect |
| 128. #2163 | D71 | semidirect |
| 131. C71 | #11663 | semidirect |
| 144. #346 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D568 | 2 |
| #22587096 | 2 |
| #22586308 | 2 |
| C71×#2163 | 2 |
| #11663 | 71 |