Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22558410 | C2 | semidirect |
| 4. Dic67⋊C32 | C2 | semidirect |
| 7. C67×#1424 | C2 | semidirect |
| 23. D1072 | Q8 | semidirect |
| 83. #1424 | D67 | semidirect |
| 87. C67 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562483 | 2 |
| #22562055 | 2 |
| #22558410 | 2 |
| Dic67⋊C32 | 2 |
| #22558388 | 2 |
| #22558386 | 2 |
| C67×#1424 | 2 |
| #13705 | 67 |