Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 88 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×#17989484 | C2 | semidirect |
| 2. C2×#17989455 | C2 | semidirect |
| 3. #22624901 | C2 | direct (N × H) |
| 8. #17989484 | C22 | semidirect |
| 10. #17989455 | C22 | semidirect |
| 15. #17988837 | C4 | semidirect |
| 17. C2×#14556523 | C4 | semidirect |
| 19. C22×D8×C73 | C4 | semidirect |
| 46. #14556523 | C2×C4 | semidirect |
| 53. C2×D8×C73 | C2×C4 | semidirect |
| 173. C2×C73 | #1339 | semidirect |
| 181. C73 | C2×#1339 | semidirect |
| 182. C22×D8 | #64408 | semidirect |
| 203. C2×D8 | C2×#64408 | semidirect |
| 351. C2 | #22624901 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989484 | 2 |
| C2×#17989455 | 2 |
| #22624901 | 2 |
| C2×#17988837 | 2 |
| C2×#1339 | 73 |