Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#17989682 | C2 | semidirect |
| 2. C2×#17989676 | C2 | semidirect |
| 3. #22626979 | C2 | direct (N × H) |
| 8. #17989682 | C22 | semidirect |
| 10. #17989676 | C22 | semidirect |
| 44. C2×D584 | C8 | semidirect |
| 48. D8×D73 | C8 | semidirect |
| 51. C2×D8×C73 | C8 | semidirect |
| 82. D584 | C2×C8 | semidirect |
| 92. D8×C73 | C2×C8 | semidirect |
| 153. C2×C73 | #1333 | semidirect |
| 156. D73 | #1333 | semidirect |
| 163. C73 | C2×#1333 | semidirect |
| 187. C2×D8 | #10596842 | semidirect |
| 231. D8 | C2×#10596842 | semidirect |
| 315. C2 | #22626979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989682 | 2 |
| C2×#17989676 | 2 |
| #22626979 | 2 |
| C2×D8×#64408 | 2 |
| C2×#1333 | 73 |