Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
782 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 309 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. C2×#17989692 | C2 | direct (N × H) |
| 7. #17989692 | C22 | direct (N × H) |
| 78. C22×C73 | #364 | semidirect |
| 90. C2×C73 | C2×#364 | semidirect |
| 97. C73 | C22×#364 | semidirect |
| 176. C22 | #17989692 | direct (N × H) |
| 185. C2 | C2×#17989692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556688 | 2 |
| C2×#17989692 | 2 |
| C22×C8×#64408 | 2 |
| C22×#364 | 73 |