Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22578373 | C2 | semidirect |
| 2. #22578246 | C2 | semidirect |
| 6. C22⋊#11764047 | C22 | semidirect |
| 61. C23×C137 | M16 | semidirect |
| 91. C137 | #1462 | semidirect |
| 142. C23 | #14555519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578373 | 2 |
| #22578246 | 2 |
| C22×C22⋊Dic137 | 2 |
| #1462 | 137 |