Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1154 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 351 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. #22623034 | C2 | semidirect |
| 3. #22611678 | C2 | semidirect |
| 4. C2×#17988399 | C2 | semidirect |
| 5. C73×#2916 | C2 | semidirect |
| 13. C2×#14556531 | C22 | semidirect |
| 14. #17988402 | C22 | semidirect |
| 15. #17988399 | C22 | semidirect |
| 19. C2×#108×C73 | C22 | semidirect |
| 118. #2916 | D73 | semidirect |
| 121. C73 | #33392 | semidirect |
| 133. C2×#108 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989392 | 2 |
| #22623034 | 2 |
| #22611678 | 2 |
| C2×#17988399 | 2 |
| C73×#2916 | 2 |
| #33392 | 73 |