Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #22586998 | C2 | semidirect |
| 4. #22586838 | C2 | semidirect |
| 6. #22586171 | C2 | semidirect |
| 7. C71×#1940 | C2 | semidirect |
| 190. #1940 | D71 | semidirect |
| 196. C71 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598686 | 2 |
| #22586998 | 2 |
| #22586990 | 2 |
| #22586838 | 2 |
| #22586834 | 2 |
| #22586171 | 2 |
| C71×#1940 | 2 |
| #10547 | 71 |