Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 267 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×D8×Dic71 | C2 | semidirect |
| 2. #22590216 | C2 | direct (N × H) |
| 3. C2×#17985827 | C2 | semidirect |
| 4. C2×#17985800 | C2 | semidirect |
| 5. C2×#17985774 | C2 | semidirect |
| 10. D8×Dic71 | C22 | semidirect |
| 14. #17985827 | C22 | semidirect |
| 15. #17985800 | C22 | semidirect |
| 16. #17985774 | C22 | semidirect |
| 18. C2×D16×C71 | C4 | semidirect |
| 38. C2×D8×C71 | C2×C4 | semidirect |
| 41. D16×C71 | C2×C4 | semidirect |
| 42. C2×C16×C71 | C2×C4 | semidirect |
| 64. D8×C71 | C22×C4 | semidirect |
| 69. C16×C71 | C22×C4 | semidirect |
| 105. C2×C71 | #2177 | semidirect |
| 114. C71 | C2×#2177 | semidirect |
| 117. C2×D16 | Dic71 | semidirect |
| 133. C2×D8 | C2×Dic71 | semidirect |
| 142. D16 | C2×Dic71 | semidirect |
| 145. C2×C16 | C2×Dic71 | semidirect |
| 164. D8 | C22×Dic71 | semidirect |
| 177. C16 | C22×Dic71 | semidirect |
| 212. C2 | #22590216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×Dic71 | 2 |
| #22590216 | 2 |
| C2×#17985827 | 2 |
| C2×#17985800 | 2 |
| C2×#17985774 | 2 |
| C22×D16×C71 | 2 |
| C2×#2177 | 71 |