Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 2. C2×#17986081 | C2 | semidirect |
| 3. #22590215 | C2 | direct (N × H) |
| 4. C2×#17985799 | C2 | semidirect |
| 5. C2×#17985774 | C2 | semidirect |
| 6. C2×#367×C71 | C2 | semidirect |
| 9. C2×D1136 | C4 | semidirect |
| 13. #17986081 | C22 | semidirect |
| 16. #17985799 | C22 | semidirect |
| 17. #17985774 | C22 | semidirect |
| 20. #367×C71 | C22 | semidirect |
| 25. C2×D568 | C2×C4 | semidirect |
| 32. D1136 | C2×C4 | semidirect |
| 40. C2×C16×C71 | C2×C4 | semidirect |
| 54. D568 | C22×C4 | semidirect |
| 69. C16×C71 | C22×C4 | semidirect |
| 104. C2×C71 | #2177 | semidirect |
| 111. C2×#367 | D71 | semidirect |
| 114. C71 | C2×#2177 | semidirect |
| 126. #367 | C2×D71 | semidirect |
| 145. C2×C16 | C4×D71 | semidirect |
| 177. C16 | C2×C4×D71 | semidirect |
| 212. C2 | #22590215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17986081 | 2 |
| #22590215 | 2 |
| C2×#17985799 | 2 |
| C2×#17985774 | 2 |
| C2×#367×C71 | 2 |
| C2×#2177 | 71 |