Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
370 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22586451 | C2 | semidirect |
| 5. #22586444 | C2 | semidirect |
| 6. #22586443 | C2 | semidirect |
| 7. C71×#1388 | C2 | semidirect |
| 143. #1388 | D71 | semidirect |
| 146. C71 | #12876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986046 | 2 |
| C2×#17985780 | 2 |
| #22588379 | 2 |
| #22586451 | 2 |
| #22586444 | 2 |
| #22586443 | 2 |
| C71×#1388 | 2 |
| #12876 | 71 |