Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 189 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. C4×#11924040 | C4 | semidirect |
| 39. C4×Dic73 | C16 | semidirect |
| 44. C42×C73 | C16 | semidirect |
| 85. C73 | #12590 | semidirect |
| 125. C42 | #11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11924040 | 2 |
| #22627001 | 2 |
| C42×#10596833 | 2 |
| #12590 | 73 |