Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16863218 | C2 | semidirect |
| 4. #22558323 | C2 | semidirect |
| 5. #22558316 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 140. C67 | #13502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863218 | 2 |
| #22561830 | 2 |
| #22560263 | 2 |
| #22558323 | 2 |
| #22558316 | 2 |
| #22558312 | 2 |
| C67×#1815 | 2 |
| #13502 | 67 |