Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 4. #22586413 | C2 | semidirect |
| 5. #22586412 | C2 | semidirect |
| 6. #22586411 | C2 | semidirect |
| 7. C71×#1372 | C2 | semidirect |
| 28. #14556067 | C8 | semidirect |
| 59. C71⋊C16 | C2×C8 | semidirect |
| 66. C16×C71 | C2×C8 | semidirect |
| 109. #1372 | D71 | semidirect |
| 112. C71 | #12009 | semidirect |
| 171. C16 | C8×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556067 | 2 |
| #22587087 | 2 |
| #335×D71 | 2 |
| #22586413 | 2 |
| #22586412 | 2 |
| #22586411 | 2 |
| C71×#1372 | 2 |
| #12009 | 71 |