Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3950 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3950 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×#11765852 | C2 | semidirect |
| 3. C2×#17986373 | C2 | direct (N × H) |
| 4. C22×C4×C71⋊C8 | C2 | semidirect |
| 5. C22×C4⋊Q8×C71 | C2 | semidirect |
| 9. C22×#11765852 | C22 | semidirect |
| 13. #17986373 | C22 | direct (N × H) |
| 14. C2×C4×C71⋊C8 | C22 | semidirect |
| 17. C2×C4⋊Q8×C71 | C22 | semidirect |
| 27. C2×#11765852 | C23 | semidirect |
| 28. C22×C71⋊C8 | D4 | semidirect |
| 32. C4×C71⋊C8 | C23 | semidirect |
| 40. C4⋊Q8×C71 | C23 | semidirect |
| 54. C2×C71⋊C8 | C2×D4 | semidirect |
| 63. C22×C4×C71 | SD16 | semidirect |
| 83. C2×C4×C71 | C2×SD16 | semidirect |
| 91. C71⋊C8 | C22×D4 | semidirect |
| 92. C22×C71 | #492 | semidirect |
| 101. C4×C71 | C22×SD16 | semidirect |
| 104. C2×C71 | C2×#492 | semidirect |
| 109. C22×C4⋊Q8 | D71 | semidirect |
| 113. C71 | C22×#492 | semidirect |
| 121. C2×C4⋊Q8 | C2×D71 | semidirect |
| 145. C4⋊Q8 | C22×D71 | semidirect |
| 168. C22×C4 | #11765852 | semidirect |
| 194. C2×C4 | C2×#11765852 | semidirect |
| 203. C22 | #17986373 | direct (N × H) |
| 209. C4 | C22×#11765852 | semidirect |
| 212. C2 | C2×#17986373 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765852 | 2 |
| C22×#14556125 | 2 |
| C2×#17986373 | 2 |
| C22×C4×C71⋊C8 | 2 |
| C22×C4⋊Q8×C71 | 2 |
| C22×#492 | 71 |