Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #17986201 | C2 | direct (N × H) |
| 4. C2×C4⋊(C71⋊C8) | C2 | semidirect |
| 5. C2×#14556052 | C2 | semidirect |
| 6. C2×C4⋊Q8×C71 | C2 | semidirect |
| 16. C4⋊(C71⋊C8) | C22 | semidirect |
| 17. #14556052 | C22 | semidirect |
| 20. C4⋊Q8×C71 | C22 | semidirect |
| 61. C2×C4×C71 | SD16 | semidirect |
| 86. C4×C71 | C2×SD16 | semidirect |
| 90. C2×C71 | #461 | semidirect |
| 96. C71 | C2×#461 | semidirect |
| 98. C2×C4⋊Q8 | D71 | semidirect |
| 110. C4⋊Q8 | C2×D71 | semidirect |
| 163. C2×C4 | #11765852 | semidirect |
| 183. C4 | C2×#11765852 | semidirect |
| 187. C2 | #17986201 | direct (N × H) |