Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 6. #17985777 | C4 | semidirect |
| 14. #322×C71 | C4 | semidirect |
| 15. C82×C71 | C4 | semidirect |
| 82. C71 | #7226 | semidirect |
| 93. #322 | Dic71 | semidirect |
| 94. C82 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590152 | 2 |
| #22588489 | 2 |
| C71×#1453 | 2 |
| #7226 | 71 |