Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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×#17988424 | C2 | semidirect |
| 3. #22612019 | C2 | semidirect |
| 4. #22608110 | C2 | semidirect |
| 5. #22608109 | C2 | semidirect |
| 6. #22608068 | C2 | semidirect |
| 7. C2×SD64×C73 | C2 | semidirect |
| 16. C2×#14556497 | C22 | semidirect |
| 17. #17988413 | C22 | semidirect |
| 19. C2×Q32×C73 | C22 | semidirect |
| 22. C2×C32×C73 | C22 | semidirect |
| 104. C2×D73 | SD64 | semidirect |
| 119. C2×SD64 | D73 | semidirect |
| 124. C73 | #13664 | semidirect |
| 126. C2×Q32 | C2×D73 | semidirect |
| 137. C2×C32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D73 | 2 |
| C2×#17988424 | 2 |
| #22612019 | 2 |
| #22608110 | 2 |
| #22608109 | 2 |
| #22608068 | 2 |
| C2×SD64×C73 | 2 |
| #13664 | 73 |