Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 40. #14556509 | C8 | semidirect |
| 96. #10596833 | #101 | semidirect |
| 123. C73 | C8×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989636 | 2 |
| #22625175 | 2 |
| M16×#10596833 | 2 |
| #22624777 | 2 |
| #22609726 | 2 |
| C8×#101 | 73 |