Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
560 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 32. C22⋊(C67⋊C8) | Q8 | semidirect |
| 46. #95×C67 | Q8 | semidirect |
| 194. C67 | #10569 | semidirect |
| 235. #95 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566323 | 2 |
| #22560397 | 2 |
| #22558088 | 2 |
| #22558052 | 2 |
| C67×#1442 | 2 |
| #10569 | 67 |