Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16863173 | C2 | semidirect |
| 4. #22558291 | C2 | semidirect |
| 5. C67×#1376 | C2 | semidirect |
| 14. #16863177 | C4 | semidirect |
| 34. #14523983 | C2×C4 | semidirect |
| 43. M32×C67 | C2×C4 | semidirect |
| 135. #1376 | D67 | semidirect |
| 136. C67 | #12607 | semidirect |
| 170. M32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11761611 | 2 |
| C2×#16863177 | 2 |
| C2×#16863173 | 2 |
| #22558291 | 2 |
| C67×#1376 | 2 |
| #12607 | 67 |