Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590385 | C2 | semidirect |
| 3. #22587946 | C2 | semidirect |
| 4. #22586410 | C2 | semidirect |
| 5. #22586388 | C2 | semidirect |
| 6. #22586385 | C2 | semidirect |
| 7. C8×D8×C71 | C2 | semidirect |
| 122. C8×D8 | D71 | semidirect |
| 126. C71 | #12428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590385 | 2 |
| #22590375 | 2 |
| #22587946 | 2 |
| #22586410 | 2 |
| #22586388 | 2 |
| #22586385 | 2 |
| C8×D8×C71 | 2 |
| #12428 | 71 |