Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
176 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22562483 | C2 | semidirect |
| 3. #22558411 | C2 | semidirect |
| 4. #22558410 | C2 | semidirect |
| 5. Dic67⋊C32 | C2 | semidirect |
| 30. D16×C67 | Q8 | semidirect |
| 87. C67 | #13705 | semidirect |
| 103. D16 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562483 | 2 |
| D16×Dic67 | 2 |
| #22558411 | 2 |
| #22558410 | 2 |
| Dic67⋊C32 | 2 |
| #22558387 | 2 |
| C67×#1415 | 2 |
| #13705 | 67 |