Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 2. #22625039 | C2 | semidirect |
| 3. #22625038 | C2 | semidirect |
| 5. #17989518 | C4 | semidirect |
| 14. #14556641 | C2×C4 | semidirect |
| 68. D73 | #1397 | semidirect |
| 73. C73 | C2×#1397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| #22625039 | 2 |
| #22625038 | 2 |
| C4×C16×D73 | 2 |
| C2×#1397 | 73 |