Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
698 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 698 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. #22592833 | C2 | semidirect |
| 2. #22592812 | C2 | semidirect |
| 3. #22588418 | C2 | semidirect |
| 4. #22586856 | C2 | semidirect |
| 5. #22586856 | C2 | semidirect |
| 6. #22586225 | C2 | semidirect |
| 222. C71 | #10328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22592833 | 2 |
| #22592812 | 2 |
| #22588418 | 2 |
| #22586856 | 2 |
| #22586225 | 2 |
| C71×#3192 | 2 |
| #10328 | 71 |