Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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⋊#14555485 | C2 | semidirect |
| 24. C23×C137 | C16 | semidirect |
| 57. C137 | #1314 | semidirect |
| 82. C23 | #14555485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊#14555485 | 2 |
| C2×C22⋊C8×C137 | 2 |
| #1314 | 137 |