Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#16863774 | C2 | semidirect |
| 4. C2×#16863211 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 7. C2×#362×C67 | C2 | semidirect |
| 198. C2×#362 | D67 | semidirect |
| 201. C67 | #13333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863839 | 2 |
| C2×#16863837 | 2 |
| C2×#16863774 | 2 |
| C2×#16863211 | 2 |
| #22561095 | 2 |
| #22558290 | 2 |
| C2×#362×C67 | 2 |
| #13333 | 67 |