Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×#17985838 | C2 | semidirect |
| 2. #22590431 | C2 | semidirect |
| 4. #22586542 | C2 | semidirect |
| 5. #22586522 | C2 | semidirect |
| 6. #22586519 | C2 | semidirect |
| 7. C22×C32×C71 | C2 | semidirect |
| 39. C32×C71 | D4 | semidirect |
| 79. C22×C71 | SD64 | semidirect |
| 97. C22×C32 | D71 | semidirect |
| 103. C71 | #13696 | semidirect |
| 135. C32 | C22⋊D71 | semidirect |
| 178. C22 | #17985838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985838 | 2 |
| #22590431 | 2 |
| #22590426 | 2 |
| #22586542 | 2 |
| #22586522 | 2 |
| #22586519 | 2 |
| C22×C32×C71 | 2 |
| #13696 | 71 |