Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1006 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 255 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×#17986120 | C2 | semidirect |
| 3. #22597051 | C2 | semidirect |
| 4. #22589226 | C2 | semidirect |
| 5. #22589171 | C2 | semidirect |
| 6. #22588028 | C2 | semidirect |
| 7. C71×#1849 | C2 | semidirect |
| 11. #17986393 | C4 | semidirect |
| 12. #17986388 | C4 | semidirect |
| 44. #14556038 | D4 | semidirect |
| 126. #1849 | D71 | semidirect |
| 128. C71 | #21709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598786 | 2 |
| C2×#17986120 | 2 |
| #22597051 | 2 |
| #22589226 | 2 |
| #22589171 | 2 |
| #22588028 | 2 |
| C71×#1849 | 2 |
| #21709 | 71 |