Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22611981 | C2 | semidirect |
| 3. Q16×#10596831 | C2 | semidirect |
| 4. #22608000 | C2 | semidirect |
| 5. #22607981 | C2 | semidirect |
| 120. C73 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611981 | 2 |
| #22609536 | 2 |
| Q16×#10596831 | 2 |
| #22608000 | 2 |
| #22607981 | 2 |
| #22607977 | 2 |
| C73×#2207 | 2 |
| #12429 | 73 |