Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1334 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 571 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×#17985748 | C2 | direct (N × H) |
| 7. #17985748 | C22 | direct (N × H) |
| 72. C22×C71 | #333 | semidirect |
| 83. C2×C71 | C2×#333 | semidirect |
| 89. C71 | C22×#333 | semidirect |
| 158. C22 | #17985748 | direct (N × H) |
| 168. C2 | C2×#17985748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C71⋊C8) | 2 |
| C2×#17985748 | 2 |
| C22×C4⋊Q8×C71 | 2 |
| C22×#333 | 71 |