Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #22587937 | C2 | semidirect |
| 4. #22586404 | C2 | semidirect |
| 5. #22586399 | C2 | semidirect |
| 6. #22586388 | C2 | semidirect |
| 88. C8×C71 | SD32 | semidirect |
| 115. C71 | #12420 | semidirect |
| 196. C8 | #14556072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590487 | 2 |
| #22590385 | 2 |
| #22587937 | 2 |
| #22586404 | 2 |
| #22586399 | 2 |
| #22586388 | 2 |
| C8×D8×C71 | 2 |
| #12420 | 71 |