Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
830 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16863554 | C2 | semidirect |
| 4. C2×#16863134 | C2 | semidirect |
| 6. #22558479 | C2 | semidirect |
| 7. C67×#1280 | C2 | semidirect |
| 253. #1280 | D67 | semidirect |
| 254. C67 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863554 | 2 |
| C2×#16863537 | 2 |
| #22566137 | 2 |
| C2×#16863134 | 2 |
| C2×#16863131 | 2 |
| #22558479 | 2 |
| C67×#1280 | 2 |
| #9965 | 67 |