Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #22590249 | C2 | semidirect |
| 3. #22587700 | C2 | semidirect |
| 4. #22586413 | C2 | semidirect |
| 5. #22586386 | C2 | semidirect |
| 6. #22586385 | C2 | semidirect |
| 7. C71×#1668 | C2 | semidirect |
| 55. C71⋊C16 | SD16 | semidirect |
| 120. #1668 | D71 | semidirect |
| 124. C71 | #12442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590589 | 2 |
| #22590249 | 2 |
| #22587700 | 2 |
| #22586413 | 2 |
| #22586386 | 2 |
| #22586385 | 2 |
| C71×#1668 | 2 |
| #12442 | 71 |