Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
702 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 3. #22588904 | C2 | semidirect |
| 4. #22588485 | C2 | semidirect |
| 5. C8×Dic71⋊C4 | C2 | semidirect |
| 7. C71×#1726 | C2 | semidirect |
| 123. #1726 | D71 | semidirect |
| 124. C71 | #21668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591638 | 2 |
| #22588953 | 2 |
| #22588904 | 2 |
| #22588485 | 2 |
| C8×Dic71⋊C4 | 2 |
| C8×(C2×D71)⋊C4 | 2 |
| C71×#1726 | 2 |
| #21668 | 71 |