Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
3870 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 3870 conjugacy classes of subgroups — too many to draw. Only its 2232 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⋊#10596833 | C2 | direct (N × H) |
| 6. C2×C4⋊#10596833 | C22 | direct (N × H) |
| 14. C4⋊#10596833 | C23 | direct (N × H) |
| 24. C23×C4×C73 | C8 | semidirect |
| 41. C22×C4×C73 | C2×C8 | semidirect |
| 43. C23×C73 | C4⋊C8 | semidirect |
| 48. C2×C4×C73 | C22×C8 | semidirect |
| 58. C22×C73 | C2×C4⋊C8 | semidirect |
| 63. C4×C73 | C23×C8 | semidirect |
| 69. C2×C73 | C22×C4⋊C8 | semidirect |
| 76. C73 | C23×C4⋊C8 | semidirect |
| 92. C23×C4 | #10596833 | semidirect |
| 110. C22×C4 | C2×#10596833 | semidirect |
| 116. C23 | C4⋊#10596833 | direct (N × H) |
| 128. C2×C4 | C22×#10596833 | semidirect |
| 131. C22 | C2×C4⋊#10596833 | direct (N × H) |
| 140. C4 | C23×#10596833 | semidirect |
| 141. C2 | C22×C4⋊#10596833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596833 | 2 |
| C22×C4⋊#10596833 | 2 |
| C23×C4×Dic73 | 2 |
| C23×C4⋊C8 | 73 |