Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 7. C2×C4×#10596842 | C4 | semidirect |
| 9. (C2×#10596842)⋊C4 | C4 | semidirect |
| 35. (C2×#64408)⋊C4 | C8 | semidirect |
| 39. #14556498 | C8 | semidirect |
| 40. #95×C73 | C8 | semidirect |
| 202. C73 | #7024 | semidirect |
| 239. #95 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C4×C22⋊#10596842 | 2 |
| #22625106 | 2 |
| #7024 | 73 |