Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
510 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 151 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×#16863174 | C2 | semidirect |
| 4. #22558288 | C2 | semidirect |
| 5. C2×#347×C67 | C2 | semidirect |
| 15. (C2×D67)⋊C16 | C4 | semidirect |
| 37. C2×C67⋊C16 | C2×C4 | semidirect |
| 47. C2×C16×C67 | C2×C4 | semidirect |
| 122. C2×D67 | #347 | semidirect |
| 139. C2×#347 | D67 | semidirect |
| 141. C67 | #12605 | semidirect |
| 179. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D67 | 2 |
| #22561819 | 2 |
| C2×#16863174 | 2 |
| #22558288 | 2 |
| C2×#347×C67 | 2 |
| #12605 | 67 |