Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14556071 | C2 | semidirect |
| 2. C22×#14556069 | C2 | semidirect |
| 3. C2×#17986376 | C2 | semidirect |
| 4. #22590607 | C2 | direct (N × H) |
| 5. C2×#17985775 | C2 | semidirect |
| 6. C2×#495×C71 | C2 | semidirect |
| 11. C2×#14556071 | C22 | semidirect |
| 13. C2×#14556069 | C22 | semidirect |
| 16. #17986376 | C22 | semidirect |
| 17. #17985775 | C22 | semidirect |
| 23. #495×C71 | C22 | semidirect |
| 37. C2×C71⋊C16 | D4 | semidirect |
| 68. C71⋊C16 | C2×D4 | semidirect |
| 138. C2×C71 | #2250 | semidirect |
| 144. C2×#495 | D71 | semidirect |
| 148. C71 | C2×#2250 | semidirect |
| 162. #495 | C2×D71 | semidirect |
| 280. C2 | #22590607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556071 | 2 |
| C22×#14556069 | 2 |
| C2×#17986376 | 2 |
| #22590607 | 2 |
| C2×#17985775 | 2 |
| C2×#495×C71 | 2 |
| C2×#2250 | 71 |