Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
494 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 116 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. #22626146 | C2 | semidirect |
| 4. #22624974 | C2 | semidirect |
| 15. #17989484 | C4 | semidirect |
| 16. #17989483 | C4 | semidirect |
| 21. #17988369 | C4 | semidirect |
| 22. #17988368 | C4 | semidirect |
| 23. #349×C73 | C4 | semidirect |
| 38. #14556665 | C2×C4 | semidirect |
| 54. #14556531 | C2×C4 | semidirect |
| 58. M32×C73 | C2×C4 | semidirect |
| 173. C73 | #12607 | semidirect |
| 189. #349 | #64408 | semidirect |
| 218. M32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#64408 | 2 |
| #22626165 | 2 |
| #22626146 | 2 |
| #22624974 | 2 |
| #349×D73 | 2 |
| #12607 | 73 |