Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2022 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 400 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×#14556658 | C2 | semidirect |
| 2. C2×#17989445 | C2 | direct (N × H) |
| 6. C2×#14556658 | C22 | semidirect |
| 7. #17989445 | C22 | direct (N × H) |
| 18. #14556658 | C23 | semidirect |
| 104. C22×C73 | #331 | semidirect |
| 118. C2×C73 | C2×#331 | semidirect |
| 125. C73 | C22×#331 | semidirect |
| 229. C22 | #17989445 | direct (N × H) |
| 240. C2 | C2×#17989445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556658 | 2 |
| C2×#17989445 | 2 |
| C22×#14556587 | 2 |
| C22×#331 | 73 |