Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 23. C4×#10596831 | C8 | semidirect |
| 24. C8×Dic73 | C8 | semidirect |
| 25. C4×C8×C73 | C8 | semidirect |
| 88. C73 | #8785 | semidirect |
| 110. C4×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| #22626937 | 2 |
| C4×C8×#64408 | 2 |
| #8785 | 73 |