Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D1072 | C2 | semidirect |
| 3. #22558408 | C2 | semidirect |
| 4. #22558387 | C2 | semidirect |
| 5. #22558386 | C2 | semidirect |
| 6. C4×C67⋊C32 | C2 | semidirect |
| 7. C4×D16×C67 | C2 | semidirect |
| 10. #16863231 | C4 | direct (N × H) |
| 23. D1072 | C2×C4 | semidirect |
| 27. C67⋊C32 | C2×C4 | semidirect |
| 31. D16×C67 | C2×C4 | semidirect |
| 80. C4×C67 | D32 | semidirect |
| 92. C4×D16 | D67 | semidirect |
| 97. C67 | C4×D32 | semidirect |
| 117. D16 | C4×D67 | semidirect |
| 171. C4 | #16863231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863231 | 2 |
| C4×D1072 | 2 |
| #22558408 | 2 |
| #22558387 | 2 |
| #22558386 | 2 |
| C4×C67⋊C32 | 2 |
| C4×D16×C67 | 2 |
| C4×D32 | 67 |