Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22558243 | C2 | direct (N × H) |
| 114. C2×C67 | #1356 | semidirect |
| 120. C67 | C2×#1356 | semidirect |
| 229. C2 | #22558243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863765 | 2 |
| C2×#16863174 | 2 |
| #22558243 | 2 |
| C2×#347×C67 | 2 |
| C2×#1356 | 67 |