Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22558968 | C2 | semidirect |
| 3. #22558171 | C2 | semidirect |
| 4. C2×C4×C16×C67 | C2 | semidirect |
| 126. C2×C4×C16 | D67 | semidirect |
| 129. C67 | #11671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22558968 | 2 |
| #22558171 | 2 |
| C2×C4×C16×C67 | 2 |
| #11671 | 67 |