Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. #22625140 | C2 | semidirect |
| 4. C8×#11924037 | C2 | semidirect |
| 5. #22624815 | C2 | semidirect |
| 6. #22624815 | C2 | semidirect |
| 191. C73 | #8245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625434 | 2 |
| #22625385 | 2 |
| #22625140 | 2 |
| C8×#11924037 | 2 |
| #22624815 | 2 |
| #22618639 | 2 |
| #8245 | 73 |