Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
196 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22590591 | C2 | semidirect |
| 5. #22586537 | C2 | semidirect |
| 6. #22586532 | C2 | semidirect |
| 7. C71×#1420 | C2 | semidirect |
| 101. #1420 | D71 | semidirect |
| 102. C71 | #13693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590660 | 2 |
| #22590658 | 2 |
| #22590591 | 2 |
| #22590220 | 2 |
| #22586537 | 2 |
| #22586532 | 2 |
| C71×#1420 | 2 |
| #13693 | 71 |