Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 32. #14556648 | C8 | semidirect |
| 37. C22⋊#10596831 | C8 | semidirect |
| 39. C22⋊C8×C73 | C8 | semidirect |
| 178. C73 | #7029 | semidirect |
| 213. C22⋊C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| C22⋊C8×#64408 | 2 |
| #7029 | 73 |