Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #22562055 | C2 | semidirect |
| 3. #22558386 | C2 | semidirect |
| 4. C32×Dic67 | C2 | semidirect |
| 5. C67×#1423 | C2 | semidirect |
| 8. D2144 | C4 | semidirect |
| 17. D1072 | C2×C4 | semidirect |
| 24. C32×C67 | C2×C4 | semidirect |
| 56. Dic67 | D32 | semidirect |
| 64. #1423 | D67 | semidirect |
| 67. C67 | C4×D32 | semidirect |
| 86. C32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2144 | 2 |
| #22562055 | 2 |
| #22558386 | 2 |
| C32×Dic67 | 2 |
| C67×#1423 | 2 |
| C4×D32 | 67 |