Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 149 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. #64408⋊C32 | C2 | direct (N × H) |
| 4. #17989694 | C4 | semidirect |
| 6. C2×#14556681 | C4 | semidirect |
| 12. #14556681 | C2×C4 | semidirect |
| 44. C2×#64408 | C32 | semidirect |
| 61. #64408 | C2×C32 | semidirect |
| 67. C2×C73 | C4×C32 | semidirect |
| 69. D73 | C4×C32 | semidirect |
| 74. C73 | C2×C4×C32 | semidirect |
| 139. C2 | #64408⋊C32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989694 | 2 |
| #64408⋊C32 | 2 |
| C2×C16×#64408 | 2 |
| C2×C4×C32 | 73 |