Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
4638 conjugacy classes of subgroups; only the 2437 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 2437 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 |
|---|---|---|
| 2. C22×C4×#10596842 | C2 | direct (N × H) |
| 4. C23×#10596842 | C4 | direct (N × H) |
| 6. C2×C4×#10596842 | C22 | direct (N × H) |
| 12. C22×#10596842 | C2×C4 | direct (N × H) |
| 14. C4×#10596842 | C23 | direct (N × H) |
| 15. C23×#64408 | C8 | semidirect |
| 23. C23×Dic73 | C8 | semidirect |
| 24. C22×C4×D73 | C8 | semidirect |
| 26. C23×C4×C73 | C8 | semidirect |
| 27. C2×#10596842 | C22×C4 | direct (N × H) |
| 30. C22×#64408 | C2×C8 | semidirect |
| 41. C22×Dic73 | C2×C8 | semidirect |
| 42. C2×C4×D73 | C2×C8 | semidirect |
| 45. C22×C4×C73 | C2×C8 | semidirect |
| 46. C23×C73 | C4×C8 | semidirect |
| 48. C22×D73 | C4×C8 | semidirect |
| 54. C2×#64408 | C22×C8 | semidirect |
| 59. #10596842 | C23×C4 | direct (N × H) |
| 60. C2×C4×C73 | C22×C8 | semidirect |
| 61. C2×Dic73 | C22×C8 | semidirect |
| 62. C4×D73 | C22×C8 | semidirect |
| 64. C22×C73 | C2×C4×C8 | semidirect |
| 66. C2×D73 | C2×C4×C8 | semidirect |
| 72. #64408 | C23×C8 | semidirect |
| 74. C4×C73 | C23×C8 | semidirect |
| 75. Dic73 | C23×C8 | semidirect |
| 77. C2×C73 | C22×C4×C8 | semidirect |
| 79. D73 | C22×C4×C8 | semidirect |
| 85. C73 | C23×C4×C8 | semidirect |
| 103. C23×C4 | #10596842 | direct (N × H) |
| 123. C22×C4 | C2×#10596842 | direct (N × H) |
| 133. C23 | C4×#10596842 | direct (N × H) |
| 144. C2×C4 | C22×#10596842 | direct (N × H) |
| 151. C22 | C2×C4×#10596842 | direct (N × H) |
| 157. C4 | C23×#10596842 | direct (N × H) |
| 161. C2 | C22×C4×#10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596842 | 2 |
| C22×C4×#10596842 | 2 |
| C23×C4×#64408 | 2 |
| C23×C4×C8 | 73 |