Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22589320 | C2 | semidirect |
| 4. #22586905 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 10. #17986371 | C4 | semidirect |
| 11. #17986345 | C4 | semidirect |
| 29. #14556128 | C2×C4 | semidirect |
| 30. #14556128 | C2×C4 | semidirect |
| 48. C4×C71⋊C8 | C2×C4 | semidirect |
| 93. C4×Dic71 | SD16 | semidirect |
| 202. C71 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599281 | 2 |
| #22591066 | 2 |
| #22589320 | 2 |
| #22586905 | 2 |
| #22586200 | 2 |
| #22586168 | 2 |
| C71×#1545 | 2 |
| #9295 | 71 |