Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
738 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #22588274 | C2 | semidirect |
| 4. #22586207 | C2 | semidirect |
| 13. #17985919 | C4 | semidirect |
| 14. #17985911 | C4 | semidirect |
| 110. C23×C71 | #103 | semidirect |
| 133. C2×C4×C71 | #103 | semidirect |
| 189. C71 | #9467 | semidirect |
| 294. C23 | #14556051 | semidirect |
| 328. C2×C4 | #14556051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597364 | 2 |
| #22591705 | 2 |
| #22588274 | 2 |
| #22586207 | 2 |
| C71×#1799 | 2 |
| #9467 | 71 |