Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
442 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626822 | C2 | semidirect |
| 2. #22625451 | C2 | semidirect |
| 3. #22625421 | C2 | semidirect |
| 4. #22625238 | C2 | semidirect |
| 5. #22624795 | C2 | semidirect |
| 6. #22624787 | C2 | semidirect |
| 226. C73 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626822 | 2 |
| #22625451 | 2 |
| #22625421 | 2 |
| #22625238 | 2 |
| #22624795 | 2 |
| #22624787 | 2 |
| #22620927 | 2 |
| #9371 | 73 |