Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 189 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. C4×#14556681 | C2 | direct (N × H) |
| 4. C2×#14556681 | C4 | direct (N × H) |
| 11. #14556681 | C2×C4 | direct (N × H) |
| 36. C2×C4×C73 | C32 | semidirect |
| 50. C4×C73 | C2×C32 | semidirect |
| 54. C2×C73 | C4×C32 | semidirect |
| 60. C73 | C2×C4×C32 | semidirect |
| 93. C2×C4 | #14556681 | direct (N × H) |
| 107. C4 | C2×#14556681 | direct (N × H) |
| 110. C2 | C4×#14556681 | 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 |
| C4×#14556681 | 2 |
| C2×C4×#11924031 | 2 |
| C2×C4×C32 | 73 |