Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22626898 | C2 | semidirect |
| 2. #22626175 | C2 | semidirect |
| 3. #22626173 | C2 | semidirect |
| 4. #22626169 | C2 | semidirect |
| 5. #22624978 | C2 | semidirect |
| 6. #22624972 | C2 | semidirect |
| 189. C73 | #12986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626898 | 2 |
| #22626175 | 2 |
| #22626173 | 2 |
| #22626169 | 2 |
| #22624978 | 2 |
| #22624972 | 2 |
| C2×#17988706 | 2 |
| #12986 | 73 |