Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
330 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22587115 | C2 | semidirect |
| 4. #22586236 | C2 | semidirect |
| 5. #22586199 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 154. C71 | #10637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588350 | 2 |
| #22588332 | 2 |
| #22587115 | 2 |
| #22586236 | 2 |
| #22586199 | 2 |
| C71×#1478 | 2 |
| #10637 | 71 |