Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
6734 conjugacy classes of subgroups; only the 640 normal subgroups are shown.
This group has 6734 conjugacy classes of subgroups — too many to draw. Only its 640 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×C22⋊C4×#64408 | C2 | semidirect |
| 4. #22625104 | C2 | semidirect |
| 7. C24×#64408 | C4 | semidirect |
| 11. C22×C4×#64408 | C22 | semidirect |
| 12. #17989528 | C4 | semidirect |
| 14. C2×(C2×#64408)⋊C4 | C22 | semidirect |
| 17. #17988443 | C4 | semidirect |
| 18. #17988442 | C4 | semidirect |
| 19. #379×C73 | C4 | semidirect |
| 33. C2×C22⋊#64408 | C2×C4 | semidirect |
| 43. C2×C22⋊Dic73 | C2×C4 | semidirect |
| 44. C2×#11924005 | C2×C4 | semidirect |
| 48. C2×C22⋊C4×C73 | C2×C4 | semidirect |
| 58. C22×#64408 | C22⋊C4 | semidirect |
| 61. C22×#64408 | C22×C4 | semidirect |
| 75. C23×D73 | C42 | semidirect |
| 82. C22×Dic73 | C22×C4 | semidirect |
| 88. C24×C73 | C42 | semidirect |
| 90. C22×C4×C73 | C22×C4 | semidirect |
| 137. C22×C73 | C4×C22⋊C4 | semidirect |
| 147. C2×D73 | C4×C22⋊C4 | semidirect |
| 155. #64408 | #379 | direct (N × H) |
| 171. C73 | C4×#379 | semidirect |
| 183. #379 | #64408 | direct (N × H) |
| 212. C2×C22⋊C4 | C2×#64408 | semidirect |
| 232. C24 | C4×#64408 | semidirect |
| 252. C22×C4 | C22×#64408 | semidirect |
| 316. C22 | C22⋊C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#64408 | 2 |
| C2×#17989528 | 2 |
| C2×C22⋊C4×#64408 | 2 |
| #22625104 | 2 |
| #379×D73 | 2 |
| C4×#379 | 73 |