Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22625863 | C2 | semidirect |
| 3. #22625482 | C2 | semidirect |
| 5. #22624777 | C2 | semidirect |
| 6. #22624759 | C2 | semidirect |
| 110. M16×C73 | M16 | semidirect |
| 117. C42×C73 | M16 | semidirect |
| 196. C73 | #8841 | semidirect |
| 276. M16 | #11924038 | semidirect |
| 306. C42 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626852 | 2 |
| #22625863 | 2 |
| #22625482 | 2 |
| #22625228 | 2 |
| #22624777 | 2 |
| #22624759 | 2 |
| #22609735 | 2 |
| #8841 | 73 |