Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
278 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 16. #14556688 | C8 | semidirect |
| 24. #14556665 | C8 | semidirect |
| 31. #14556531 | C8 | semidirect |
| 34. M32×C73 | C8 | semidirect |
| 91. C73 | #7138 | semidirect |
| 113. M32 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| C2×C8×#10596842 | 2 |
| M32×#64408 | 2 |
| #7138 | 73 |