Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#16863445 | C2 | semidirect |
| 2. C2×#16863209 | C2 | semidirect |
| 3. C2×#16863178 | C2 | semidirect |
| 4. #22558307 | C2 | semidirect |
| 30. #14523979 | D4 | semidirect |
| 155. C67 | #13010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863445 | 2 |
| C2×#16863209 | 2 |
| C2×#16863178 | 2 |
| #22558307 | 2 |
| C2×#469×C67 | 2 |
| #13010 | 67 |