Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
182 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22608134 | C2 | direct (N × H) |
| 70. C2×C73 | #1425 | semidirect |
| 76. C73 | C2×#1425 | semidirect |
| 141. C2 | #22608134 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556497 | 2 |
| C2×#17988417 | 2 |
| #22608134 | 2 |
| C2×#368×C73 | 2 |
| C2×#1425 | 73 |