Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 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. C22×D1136 | C2 | semidirect |
| 2. C2×#17985834 | C2 | semidirect |
| 3. #22586517 | C2 | semidirect |
| 4. C22⋊(C71⋊C32) | C2 | semidirect |
| 5. C71×#2215 | C2 | semidirect |
| 11. C2×C71⋊C32 | C22 | semidirect |
| 12. C2×D16×C71 | C22 | semidirect |
| 15. #366×C71 | C22 | semidirect |
| 24. D1136 | D4 | semidirect |
| 81. C22×C71 | D32 | semidirect |
| 100. #2215 | D71 | semidirect |
| 103. C71 | #13661 | semidirect |
| 108. C2×D16 | C2×D71 | semidirect |
| 113. #366 | C2×D71 | semidirect |
| 183. C22 | #17985834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17985834 | 2 |
| #22586517 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C71×#2215 | 2 |
| #13661 | 71 |