Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C2×#16863744 | C2 | semidirect |
| 3. #22561049 | C2 | semidirect |
| 4. #22558890 | C2 | semidirect |
| 5. #22558660 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 7. C67×#3141 | C2 | semidirect |
| 184. #3141 | D67 | semidirect |
| 190. C67 | #10160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| C2×#16863744 | 2 |
| #22561049 | 2 |
| #22558890 | 2 |
| #22558660 | 2 |
| #22558047 | 2 |
| C67×#3141 | 2 |
| #10160 | 67 |