Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 288 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×#17985839 | C2 | semidirect |
| 2. C2×#17985837 | C2 | semidirect |
| 3. #22590431 | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 5. #22586518 | C2 | semidirect |
| 6. C22⋊(C71⋊C32) | C2 | 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×#17985839 | 2 |
| C2×#17985837 | 2 |
| #22590431 | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C2×#508×C71 | 2 |
| #13666 | 71 |