Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22593983 | C2 | semidirect |
| 5. #22586232 | C2 | semidirect |
| 6. #22586206 | C2 | semidirect |
| 7. C71×#1285 | C2 | semidirect |
| 30. #14556128 | Q8 | semidirect |
| 31. #14556125 | Q8 | semidirect |
| 188. #1285 | D71 | semidirect |
| 189. C71 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22593983 | 2 |
| #22589258 | 2 |
| #22586888 | 2 |
| #22586849 | 2 |
| #22586232 | 2 |
| #22586206 | 2 |
| C71×#1285 | 2 |
| #10378 | 71 |