Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. #22599723 | C2 | semidirect |
| 3. #22589181 | C2 | semidirect |
| 4. #22586931 | C2 | semidirect |
| 5. #22586761 | C2 | semidirect |
| 6. #22586230 | C2 | semidirect |
| 7. C71×#3138 | C2 | semidirect |
| 195. #3138 | D71 | semidirect |
| 200. C71 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599723 | 2 |
| #22599258 | 2 |
| #22589181 | 2 |
| #22586931 | 2 |
| #22586761 | 2 |
| #22586230 | 2 |
| C71×#3138 | 2 |
| #10112 | 71 |