Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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×D16×D71 | C2 | semidirect |
| 2. C2×D2272 | C2 | semidirect |
| 3. C2×#17985834 | C2 | semidirect |
| 4. #22590427 | C2 | semidirect |
| 5. #22586517 | C2 | semidirect |
| 6. (C2×D71)⋊C32 | C2 | semidirect |
| 7. C71×#1415 | C2 | semidirect |
| 10. C2×D1136 | C22 | semidirect |
| 18. C2×C71⋊C32 | C22 | semidirect |
| 21. C2×C32×C71 | C22 | semidirect |
| 22. #366×C71 | C22 | semidirect |
| 34. D1136 | D4 | semidirect |
| 43. D16×C71 | D4 | semidirect |
| 108. C2×D71 | D32 | semidirect |
| 126. #1415 | D71 | semidirect |
| 128. C71 | #13661 | semidirect |
| 141. C2×C32 | C2×D71 | semidirect |
| 142. #366 | C2×D71 | semidirect |
| 159. D16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D71 | 2 |
| C2×D2272 | 2 |
| C2×#17985834 | 2 |
| #22590427 | 2 |
| #22586517 | 2 |
| (C2×D71)⋊C32 | 2 |
| C71×#1415 | 2 |
| #13661 | 71 |