Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22627014 | C2 | semidirect |
| 3. C4×#14556681 | C2 | semidirect |
| 5. #17989694 | C4 | direct (N × H) |
| 14. #14556681 | C2×C4 | semidirect |
| 49. C4×D73 | C32 | semidirect |
| 60. C4×C73 | C2×C32 | semidirect |
| 64. Dic73 | C2×C32 | semidirect |
| 68. D73 | C4×C32 | semidirect |
| 73. C73 | C2×C4×C32 | semidirect |
| 131. C4 | #17989694 | 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 |
| #22627014 | 2 |
| C4×#14556681 | 2 |
| C4×#14556664 | 2 |
| C2×C4×C32 | 73 |