Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 5. #17989480 | C4 | direct (N × H) |
| 6. #17989475 | C4 | semidirect |
| 7. C4×#11924031 | C4 | semidirect |
| 26. #11924031 | C42 | semidirect |
| 60. C4×C73 | #347 | semidirect |
| 72. C73 | C4×#347 | semidirect |
| 130. C4 | #17989480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989480 | 2 |
| C4×#14556665 | 2 |
| C4×#14556501 | 2 |
| C4×#347 | 73 |