Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#17989441 | C2 | semidirect |
| 4. #22625211 | C2 | semidirect |
| 5. #22624814 | C2 | semidirect |
| 6. #22624768 | C2 | semidirect |
| 27. #17988918 | C4 | semidirect |
| 28. #17988898 | C4 | semidirect |
| 32. #17988743 | C4 | semidirect |
| 34. #448×C73 | C4 | semidirect |
| 241. C73 | #9263 | semidirect |
| 251. #448 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626804 | 2 |
| #22625316 | 2 |
| C2×#17989441 | 2 |
| #22625211 | 2 |
| #22624814 | 2 |
| #22624768 | 2 |
| #22620709 | 2 |
| #9263 | 73 |