Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. #22591521 | C2 | semidirect |
| 2. #22587057 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586205 | C2 | semidirect |
| 21. #487×C71 | C4 | semidirect |
| 22. #486×C71 | C4 | semidirect |
| 158. C71 | #9430 | semidirect |
| 162. #487 | Dic71 | semidirect |
| 163. #486 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591521 | 2 |
| #22587057 | 2 |
| #22586887 | 2 |
| #22586205 | 2 |
| C71×#3141 | 2 |
| #9430 | 71 |