Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22611704 | C2 | semidirect |
| 5. #22610721 | C2 | semidirect |
| 6. #22608046 | C2 | semidirect |
| 7. C73×#1378 | C2 | semidirect |
| 19. #17988401 | C4 | semidirect |
| 40. #14556527 | C2×C4 | semidirect |
| 51. M32×C73 | C2×C4 | semidirect |
| 144. #1378 | D73 | semidirect |
| 145. C73 | #12953 | semidirect |
| 181. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618784 | 2 |
| #22611704 | 2 |
| C2×#17988401 | 2 |
| #22610721 | 2 |
| #22608046 | 2 |
| C73×#1378 | 2 |
| #12953 | 73 |