Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1734 conjugacy classes of subgroups; only the 1035 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 1035 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×#14523954 | C2 | semidirect |
| 3. C42×C67⋊C8 | C2 | semidirect |
| 6. C4×#11761612 | C4 | direct (N × H) |
| 16. #14523954 | C2×C4 | semidirect |
| 17. C4×C67⋊C8 | C2×C4 | semidirect |
| 27. #11761612 | C42 | direct (N × H) |
| 39. C42×C67 | M16 | semidirect |
| 53. C67⋊C8 | C2×C42 | semidirect |
| 60. C4×C67 | C4×M16 | semidirect |
| 70. C67 | C42×M16 | semidirect |
| 105. C42 | #11761612 | direct (N × H) |
| 126. C4 | C4×#11761612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11761612 | 2 |
| C4×#14523954 | 2 |
| C42×C67⋊C8 | 2 |
| C2×C43×C67 | 2 |
| C42×M16 | 67 |