Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22586545 | C2 | semidirect |
| 4. #22586534 | C2 | semidirect |
| 5. #22586532 | C2 | semidirect |
| 7. C71×#1426 | C2 | semidirect |
| 83. #1426 | D71 | semidirect |
| 87. C71 | #13718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590449 | 2 |
| #22590133 | 2 |
| #22586545 | 2 |
| #22586534 | 2 |
| #22586532 | 2 |
| #22586479 | 2 |
| C71×#1426 | 2 |
| #13718 | 71 |