Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22587123 | C2 | semidirect |
| 5. #22586696 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1989 | C2 | semidirect |
| 171. #1989 | D71 | semidirect |
| 177. C71 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599530 | 2 |
| #22587123 | 2 |
| #22587033 | 2 |
| #22586834 | 2 |
| #22586696 | 2 |
| #22586196 | 2 |
| C71×#1989 | 2 |
| #10509 | 71 |