Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 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 |
|---|---|---|
| 1. C2×#16863834 | C2 | semidirect |
| 2. C2×#16863832 | C2 | semidirect |
| 3. C2×#16863771 | C2 | semidirect |
| 4. C2×#16863208 | C2 | semidirect |
| 5. #22561095 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 7. C2×#361×C67 | C2 | semidirect |
| 38. C2×Dic268 | D4 | semidirect |
| 46. C2×D536 | D4 | semidirect |
| 59. #14523983 | D4 | semidirect |
| 75. M32×C67 | D4 | semidirect |
| 210. C2×#361 | D67 | semidirect |
| 213. C67 | #13331 | semidirect |
| 276. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863834 | 2 |
| C2×#16863832 | 2 |
| C2×#16863771 | 2 |
| C2×#16863208 | 2 |
| #22561095 | 2 |
| #22558290 | 2 |
| C2×#361×C67 | 2 |
| #13331 | 67 |