Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1174 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 361 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 |
|---|---|---|
| 7. C2×C4×#10596842 | C4 | semidirect |
| 8. (C2×#10596842)⋊C4 | C4 | semidirect |
| 27. (C2×#64408)⋊C4 | C8 | semidirect |
| 29. #14556498 | C8 | semidirect |
| 30. #95×C73 | C8 | semidirect |
| 71. C2×#64408 | C4×C8 | semidirect |
| 82. #10596842 | #95 | direct (N × H) |
| 84. C2×C4×C73 | C4×C8 | semidirect |
| 86. C2×Dic73 | C4×C8 | semidirect |
| 120. C73 | C8×#95 | semidirect |
| 147. #95 | #10596842 | direct (N × H) |
| 204. C2×C4 | C4×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10596842 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #95×#64408 | 2 |
| C8×#95 | 73 |