Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 402 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. #22561983 | C2 | semidirect |
| 4. #22558323 | C2 | semidirect |
| 12. #16863178 | C4 | semidirect |
| 26. #14523983 | C2×C4 | semidirect |
| 126. C67 | #12932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568799 | 2 |
| #22561983 | 2 |
| C2×#16863178 | 2 |
| #22558323 | 2 |
| C67×#1811 | 2 |
| #12932 | 67 |