Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 203 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. #22562487 | C2 | direct (N × H) |
| 85. C2×C67 | #2253 | semidirect |
| 94. C67 | C2×#2253 | semidirect |
| 172. C2 | #22562487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863797 | 2 |
| #22562487 | 2 |
| C2×#16863224 | 2 |
| C2×#16863221 | 2 |
| C2×C16×Dic67 | 2 |
| C2×#367×C67 | 2 |
| C2×#2253 | 67 |