Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 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×#17985836 | C2 | semidirect |
| 3. #22590428 | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 5. #22586519 | C2 | semidirect |
| 6. (C2×D71)⋊C32 | C2 | semidirect |
| 7. C2×Q64×C71 | C2 | semidirect |
| 112. C2×Q64 | D71 | semidirect |
| 118. C71 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986432 | 2 |
| C2×#17985836 | 2 |
| #22590428 | 2 |
| #22586521 | 2 |
| #22586519 | 2 |
| (C2×D71)⋊C32 | 2 |
| C2×Q64×C71 | 2 |
| #13666 | 71 |