Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #22558383 | C2 | direct (N × H) |
| 5. C2×#14524035 | C4 | semidirect |
| 8. #16863750 | C4 | semidirect |
| 13. C2×C4×C67⋊C8 | C4 | semidirect |
| 24. #14524035 | C2×C4 | semidirect |
| 34. C4×C67⋊C8 | C2×C4 | semidirect |
| 134. C2×C67 | #1414 | semidirect |
| 140. C67 | C2×#1414 | semidirect |
| 269. C2 | #22558383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863750 | 2 |
| C2×#16863193 | 2 |
| #22558383 | 2 |
| C2×#354×C67 | 2 |
| C2×#1414 | 67 |