Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 15. #17985741 | C4 | semidirect |
| 18. #330×C71 | C4 | semidirect |
| 107. Dic71 | #330 | direct (N × H) |
| 119. C71 | C4×#330 | semidirect |
| 132. #330 | Dic71 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×Dic71 | 2 |
| #97×Dic71 | 2 |
| C2×#17985741 | 2 |
| #22586222 | 2 |
| C2×#330×C71 | 2 |
| C4×#330 | 71 |