Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
756 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 154 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. #22625965 | C2 | semidirect |
| 2. #22625962 | C2 | semidirect |
| 3. #22625938 | C2 | semidirect |
| 4. #22625934 | C2 | semidirect |
| 5. #22625861 | C2 | semidirect |
| 20. #17988975 | C4 | semidirect |
| 21. #17988963 | C4 | semidirect |
| 22. #17988960 | C4 | semidirect |
| 23. #17988959 | C4 | semidirect |
| 25. #493×C73 | C4 | semidirect |
| 41. C2×#11924017 | C2×C4 | semidirect |
| 42. C2×#11924016 | C2×C4 | semidirect |
| 43. C2×#11924013 | C2×C4 | semidirect |
| 45. #14556591 | C2×C4 | semidirect |
| 49. #14556578 | C2×C4 | semidirect |
| 53. #14556501 | C2×C4 | semidirect |
| 54. C4×#10596831 | C2×C4 | semidirect |
| 55. C2×D8×C73 | C2×C4 | semidirect |
| 57. #127×C73 | C2×C4 | semidirect |
| 58. C4×C8×C73 | C2×C4 | semidirect |
| 161. C73 | #23361 | semidirect |
| 169. #493 | #64408 | semidirect |
| 189. C2×D8 | C2×#64408 | semidirect |
| 199. #127 | C2×#64408 | semidirect |
| 213. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625965 | 2 |
| #22625962 | 2 |
| #22625938 | 2 |
| #22625934 | 2 |
| #22625861 | 2 |
| #22620382 | 2 |
| #23361 | 73 |