Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22591520 | C2 | semidirect |
| 3. #22587065 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586204 | C2 | semidirect |
| 11. #17986378 | C4 | semidirect |
| 12. #17986371 | C4 | semidirect |
| 164. C71 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598800 | 2 |
| #22591520 | 2 |
| #22587065 | 2 |
| #22586887 | 2 |
| #22586206 | 2 |
| #22586204 | 2 |
| C71×#1514 | 2 |
| #9429 | 71 |