Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22626946 | C2 | semidirect |
| 4. C16×#10596842 | C2 | semidirect |
| 18. #14556686 | C8 | semidirect |
| 21. C2×#11924040 | C8 | semidirect |
| 27. #14556666 | C8 | semidirect |
| 28. #14556665 | C8 | semidirect |
| 35. #14556531 | C8 | semidirect |
| 36. #14556530 | C8 | semidirect |
| 38. M32×C73 | C8 | semidirect |
| 97. C73 | #11399 | semidirect |
| 117. M32 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64408⋊C16 | 2 |
| #22627040 | 2 |
| #22626946 | 2 |
| C16×#10596842 | 2 |
| M32×#64408 | 2 |
| #11399 | 73 |