Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22625179 | C2 | semidirect |
| 2. C2×#17989432 | C2 | semidirect |
| 3. #22624872 | C2 | semidirect |
| 4. #22624859 | C2 | semidirect |
| 192. C73 | #11553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625179 | 2 |
| C2×#17989432 | 2 |
| #22624872 | 2 |
| #22624859 | 2 |
| #22614424 | 2 |
| #11553 | 73 |