Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#17986440 | C2 | semidirect |
| 3. #22598829 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22589236 | C2 | semidirect |
| 6. #22586425 | C2 | semidirect |
| 7. C71×#2141 | C2 | semidirect |
| 216. #2141 | D71 | semidirect |
| 219. C71 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| C2×#17986440 | 2 |
| #22598829 | 2 |
| #22590075 | 2 |
| #22589236 | 2 |
| #22586425 | 2 |
| C71×#2141 | 2 |
| #13335 | 71 |