Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 360 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. #17989473 | C4 | direct (N × H) |
| 6. C4×#11924031 | C4 | semidirect |
| 24. #11924031 | C42 | semidirect |
| 30. C4×Dic73 | C16 | semidirect |
| 55. C4×C73 | C4×C16 | semidirect |
| 59. Dic73 | C4×C16 | semidirect |
| 67. C73 | C42×C16 | semidirect |
| 120. C4 | #17989473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989473 | 2 |
| C2×C4×#11924031 | 2 |
| C4×C8×Dic73 | 2 |
| C42×C16 | 73 |