Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C22×#14556681 | C2 | semidirect |
| 2. #22627024 | C2 | direct (N × H) |
| 5. C2×#14556681 | C22 | semidirect |
| 49. C22×D73 | C32 | semidirect |
| 71. C2×D73 | C2×C32 | semidirect |
| 77. C2×C73 | C22⋊C32 | semidirect |
| 85. C73 | C2×C22⋊C32 | semidirect |
| 159. C2 | #22627024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556681 | 2 |
| #22627024 | 2 |
| C22×#14556664 | 2 |
| C2×C22⋊C32 | 73 |