Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
610 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22561049 | C2 | semidirect |
| 3. #22558968 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. C8×M16×C67 | C2 | semidirect |
| 64. M16×C67 | D8 | semidirect |
| 99. C8×C67 | #100 | semidirect |
| 126. C8×M16 | D67 | semidirect |
| 127. C67 | #9802 | semidirect |
| 185. M16 | D536 | semidirect |
| 222. C8 | #14523959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| #22561049 | 2 |
| #22558968 | 2 |
| #22558876 | 2 |
| C8×M16×C67 | 2 |
| #9802 | 67 |