Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #17986379 | C4 | semidirect |
| 11. #17986350 | C4 | semidirect |
| 102. C42×C71 | Q16 | semidirect |
| 173. C71 | #9297 | semidirect |
| 268. C42 | Dic284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599290 | 2 |
| #22591088 | 2 |
| #22589321 | 2 |
| #22587020 | 2 |
| #22586905 | 2 |
| #22586199 | 2 |
| C71×#1274 | 2 |
| #9297 | 71 |