Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
652 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22589318 | C2 | semidirect |
| 4. #22587021 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#3209 | C2 | semidirect |
| 179. #3209 | D71 | semidirect |
| 186. C71 | #10291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22596698 | 2 |
| #22589318 | 2 |
| #22587021 | 2 |
| #22587007 | 2 |
| #22586172 | 2 |
| C71×#3209 | 2 |
| #10291 | 71 |