Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626710 | C2 | semidirect |
| 2. #22626258 | C2 | semidirect |
| 3. C2×#17989505 | C2 | semidirect |
| 4. #22626092 | C2 | semidirect |
| 5. #22625009 | C2 | semidirect |
| 6. #22624983 | C2 | semidirect |
| 24. #17989025 | C4 | semidirect |
| 26. #17989023 | C4 | semidirect |
| 27. #17989022 | C4 | semidirect |
| 32. #509×C73 | C4 | semidirect |
| 224. C73 | #13032 | semidirect |
| 233. #509 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626710 | 2 |
| #22626258 | 2 |
| C2×#17989505 | 2 |
| #22626092 | 2 |
| #22625009 | 2 |
| #22624983 | 2 |
| #509×D73 | 2 |
| #13032 | 73 |