Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×Q32×D67 | C2 | semidirect |
| 2. C2×#16863235 | C2 | semidirect |
| 3. C2×#16863233 | C2 | semidirect |
| 5. #22558389 | C2 | semidirect |
| 6. (C2×D67)⋊C32 | C2 | semidirect |
| 7. C67×#1416 | C2 | semidirect |
| 32. Dic536 | D4 | semidirect |
| 43. Q32×C67 | D4 | semidirect |
| 99. C2×D67 | SD64 | semidirect |
| 117. #1416 | D67 | semidirect |
| 119. C67 | #13662 | semidirect |
| 148. Q32 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D67 | 2 |
| C2×#16863235 | 2 |
| C2×#16863233 | 2 |
| #22562296 | 2 |
| #22558389 | 2 |
| (C2×D67)⋊C32 | 2 |
| C67×#1416 | 2 |
| #13662 | 67 |