Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
592 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22607956 | C2 | semidirect |
| 4. #22607953 | C2 | semidirect |
| 6. C2×#14556570 | C4 | semidirect |
| 8. #17988523 | C4 | semidirect |
| 12. #17988499 | C4 | semidirect |
| 15. #17988447 | C4 | semidirect |
| 23. C22×Dic146 | C2×C4 | semidirect |
| 28. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 44. #14556498 | C2×C4 | semidirect |
| 45. #14556498 | C2×C4 | semidirect |
| 222. C73 | #11716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615736 | 2 |
| C2×#17988354 | 2 |
| #22607956 | 2 |
| #22607953 | 2 |
| C2×#323×C73 | 2 |
| #11716 | 73 |