Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
| 3. #22586521 | C2 | semidirect |
| 75. C22×C71 | Q64 | semidirect |
| 93. C71 | #13665 | semidirect |
| 163. C22 | #17985839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985839 | 2 |
| #22590431 | 2 |
| #22586521 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C22×Q32×C71 | 2 |
| #13665 | 71 |