Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 9. #17986402 | C4 | semidirect |
| 10. #17986378 | C4 | semidirect |
| 11. #17986351 | C4 | semidirect |
| 12. #17986349 | C4 | semidirect |
| 101. C42×C71 | Q16 | semidirect |
| 161. C71 | #9848 | semidirect |
| 255. C42 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598922 | 2 |
| #22589317 | 2 |
| #22588086 | 2 |
| #22587098 | 2 |
| #22586795 | 2 |
| #22586794 | 2 |
| C71×#1994 | 2 |
| #9848 | 71 |