Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C2×#16863712 | C2 | semidirect |
| 2. C2×#16863707 | C2 | semidirect |
| 3. #22560287 | C2 | semidirect |
| 4. #22558569 | C2 | semidirect |
| 5. #22558569 | C2 | semidirect |
| 6. #22558096 | C2 | semidirect |
| 210. C67 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863712 | 2 |
| C2×#16863707 | 2 |
| #22560287 | 2 |
| #22558569 | 2 |
| #22558096 | 2 |
| C67×#3192 | 2 |
| #9992 | 67 |