Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2046 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1077 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. C42×#10596842 | C2 | direct (N × H) |
| 5. C2×C4×#10596842 | C4 | direct (N × H) |
| 14. C4×#10596842 | C2×C4 | direct (N × H) |
| 17. C2×C4×#64408 | C8 | semidirect |
| 23. C2×C4×Dic73 | C8 | semidirect |
| 24. C42×D73 | C8 | semidirect |
| 26. C2×C42×C73 | C8 | semidirect |
| 27. C2×#10596842 | C42 | direct (N × H) |
| 36. C4×#64408 | C2×C8 | semidirect |
| 44. C4×Dic73 | C2×C8 | semidirect |
| 46. C42×C73 | C2×C8 | semidirect |
| 52. C2×#64408 | C4×C8 | semidirect |
| 58. #10596842 | C2×C42 | direct (N × H) |
| 59. C2×C4×C73 | C4×C8 | semidirect |
| 61. C2×Dic73 | C4×C8 | semidirect |
| 63. C4×D73 | C4×C8 | semidirect |
| 74. #64408 | C2×C4×C8 | semidirect |
| 76. C4×C73 | C2×C4×C8 | semidirect |
| 77. Dic73 | C2×C4×C8 | semidirect |
| 79. C2×C73 | C42×C8 | semidirect |
| 81. D73 | C42×C8 | semidirect |
| 87. C73 | C2×C42×C8 | semidirect |
| 109. C2×C42 | #10596842 | direct (N × H) |
| 130. C42 | C2×#10596842 | direct (N × H) |
| 147. C2×C4 | C4×#10596842 | direct (N × H) |
| 161. C4 | C2×C4×#10596842 | direct (N × H) |
| 165. C2 | C42×#10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10596842 | 2 |
| C42×#10596842 | 2 |
| C2×C42×#64408 | 2 |
| C2×C42×C8 | 73 |