Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16863209 | C2 | semidirect |
| 2. #22561945 | C2 | semidirect |
| 3. #22561937 | C2 | semidirect |
| 4. #22561925 | C2 | semidirect |
| 5. #22561814 | C2 | semidirect |
| 6. #22560333 | C2 | semidirect |
| 24. #495×C67 | C4 | semidirect |
| 25. #493×C67 | C4 | semidirect |
| 32. #14523983 | D4 | semidirect |
| 34. C2×C67⋊C16 | D4 | semidirect |
| 182. C67 | #13215 | semidirect |
| 190. #495 | Dic67 | semidirect |
| 191. #493 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863209 | 2 |
| #22561945 | 2 |
| #22561937 | 2 |
| #22561925 | 2 |
| #22561814 | 2 |
| #22560333 | 2 |
| C67×#3155 | 2 |
| #13215 | 67 |