Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22587025 | C2 | semidirect |
| 5. #22587021 | C2 | semidirect |
| 6. #22586173 | C2 | semidirect |
| 7. C71×#2868 | C2 | semidirect |
| 112. C42×C71 | SD16 | semidirect |
| 177. #2868 | D71 | semidirect |
| 182. C71 | #10283 | semidirect |
| 287. C42 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599468 | 2 |
| #22599265 | 2 |
| #22589168 | 2 |
| #22587025 | 2 |
| #22587021 | 2 |
| #22586173 | 2 |
| C71×#2868 | 2 |
| #10283 | 71 |