Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569248 | C2 | semidirect |
| 3. #22560129 | C2 | semidirect |
| 4. #22560129 | C2 | semidirect |
| 5. #22558545 | C2 | semidirect |
| 6. #22558115 | C2 | semidirect |
| 7. C67×#1305 | C2 | semidirect |
| 41. C2×#11761612 | D4 | semidirect |
| 67. C2×M16×C67 | D4 | semidirect |
| 190. C2×Dic67 | #100 | semidirect |
| 255. #1305 | D67 | semidirect |
| 256. C67 | #9504 | semidirect |
| 294. C2×M16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569248 | 2 |
| #22563566 | 2 |
| #22560129 | 2 |
| #22558545 | 2 |
| #22558115 | 2 |
| C67×#1305 | 2 |
| #9504 | 67 |