Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
584 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22598372 | C2 | semidirect |
| 3. #22598367 | C2 | semidirect |
| 4. #22589279 | C2 | semidirect |
| 5. #22586738 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1480 | C2 | semidirect |
| 106. C2×C71⋊C8 | SD16 | semidirect |
| 214. #1480 | D71 | semidirect |
| 216. C71 | #10034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598785 | 2 |
| #22598372 | 2 |
| #22598367 | 2 |
| #22589279 | 2 |
| #22586738 | 2 |
| #22586170 | 2 |
| C71×#1480 | 2 |
| #10034 | 71 |