Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4638 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 987 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. C23×#11765850 | C2 | semidirect |
| 2. C22×#14556125 | C2 | semidirect |
| 3. C2×#17986375 | C2 | direct (N × H) |
| 4. C22×C4×C71⋊C8 | C2 | semidirect |
| 5. C22×#127×C71 | C2 | semidirect |
| 9. C22×#11765850 | C22 | semidirect |
| 12. C2×#14556125 | C22 | semidirect |
| 13. #17986375 | C22 | direct (N × H) |
| 14. C2×C4×C71⋊C8 | C22 | semidirect |
| 18. C2×#127×C71 | C22 | semidirect |
| 27. C2×#11765850 | C23 | semidirect |
| 28. C22×C71⋊C8 | D4 | semidirect |
| 31. #14556125 | C23 | semidirect |
| 32. C4×C71⋊C8 | C23 | semidirect |
| 42. #127×C71 | C23 | semidirect |
| 55. C2×C71⋊C8 | C2×D4 | semidirect |
| 67. C22×C4×C71 | D8 | semidirect |
| 89. C2×C4×C71 | C2×D8 | semidirect |
| 97. C71⋊C8 | C22×D4 | semidirect |
| 101. C22×C71 | #493 | semidirect |
| 109. C4×C71 | C22×D8 | semidirect |
| 113. C2×C71 | C2×#493 | semidirect |
| 119. C22×#127 | D71 | semidirect |
| 122. C71 | C22×#493 | semidirect |
| 133. C2×#127 | C2×D71 | semidirect |
| 158. #127 | C22×D71 | semidirect |
| 181. C22×C4 | #11765850 | semidirect |
| 209. C2×C4 | C2×#11765850 | semidirect |
| 221. C22 | #17986375 | direct (N × H) |
| 226. C4 | C22×#11765850 | semidirect |
| 230. C2 | C2×#17986375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765850 | 2 |
| C22×#14556125 | 2 |
| C2×#17986375 | 2 |
| C22×C4×C71⋊C8 | 2 |
| C22×#127×C71 | 2 |
| C22×#493 | 71 |