Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. C4⋊(C71⋊C32) | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 5. C71×#2247 | C2 | semidirect |
| 70. C4×C71 | SD64 | semidirect |
| 80. #2247 | D71 | semidirect |
| 84. C71 | #13687 | semidirect |
| 150. C4 | #17985836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985836 | 2 |
| C4×D1136 | 2 |
| C4⋊(C71⋊C32) | 2 |
| #22586521 | 2 |
| C71×#2247 | 2 |
| #13687 | 71 |