Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
924 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22599723 | C2 | semidirect |
| 3. #22587621 | C2 | semidirect |
| 4. #22587572 | C2 | semidirect |
| 5. #22587078 | C2 | semidirect |
| 6. #22586792 | C2 | semidirect |
| 7. C71×#3160 | C2 | semidirect |
| 165. #3160 | D71 | semidirect |
| 170. C71 | #18701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602740 | 2 |
| #22599723 | 2 |
| #22587621 | 2 |
| #22587572 | 2 |
| #22587078 | 2 |
| #22586792 | 2 |
| C71×#3160 | 2 |
| #18701 | 71 |