Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16863226 | C2 | semidirect |
| 4. #22561000 | C2 | semidirect |
| 5. #22558322 | C2 | semidirect |
| 6. #22558297 | C2 | semidirect |
| 23. #359×C67 | C4 | semidirect |
| 148. C67 | #12947 | semidirect |
| 163. #359 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569126 | 2 |
| C2×#16863226 | 2 |
| #22561937 | 2 |
| #22561000 | 2 |
| #22558322 | 2 |
| #22558297 | 2 |
| C2×#359×C67 | 2 |
| #12947 | 67 |