Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 72. C2×C4×C67 | Q32 | semidirect |
| 114. C67 | #13450 | semidirect |
| 191. C2×C4 | Dic536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic536 | 2 |
| C2×#16863201 | 2 |
| #22561070 | 2 |
| #22558301 | 2 |
| C2×C4⋊C16×C67 | 2 |
| #13450 | 67 |