Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
258 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. #22627006 | C2 | semidirect |
| 2. (C2×#10596842)⋊C8 | C2 | semidirect |
| 30. C2×D584 | C8 | semidirect |
| 32. C2×Q16×C73 | C8 | semidirect |
| 116. C73 | #7114 | semidirect |
| 127. C2×Q16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627006 | 2 |
| (C2×#10596842)⋊C8 | 2 |
| #22626082 | 2 |
| #7114 | 73 |