Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22599682 | C2 | semidirect |
| 4. #22586956 | C2 | semidirect |
| 5. #22586955 | C2 | semidirect |
| 6. #22586209 | C2 | semidirect |
| 206. C71 | #10030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22598439 | 2 |
| #22589139 | 2 |
| #22586956 | 2 |
| #22586955 | 2 |
| #22586209 | 2 |
| C71×#3110 | 2 |
| #10030 | 71 |