Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
326 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 105 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. #17985748 | C4 | semidirect |
| 16. #17985745 | C4 | semidirect |
| 146. C71 | #9584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588193 | 2 |
| #22587116 | 2 |
| #22586997 | 2 |
| #22586743 | 2 |
| #22586235 | 2 |
| #22586173 | 2 |
| C71×#1994 | 2 |
| #9584 | 71 |