Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
348 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. #22589334 | C2 | semidirect |
| 2. #22587108 | C2 | semidirect |
| 4. #22586942 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 173. C71 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589334 | 2 |
| #22587108 | 2 |
| #22587062 | 2 |
| #22586942 | 2 |
| #22586932 | 2 |
| #22586211 | 2 |
| C71×#3234 | 2 |
| #10497 | 71 |