Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D67 | C2 | semidirect |
| 3. #368×D67 | C2 | semidirect |
| 4. #22558400 | C2 | semidirect |
| 5. #22558399 | C2 | semidirect |
| 6. #22558398 | C2 | semidirect |
| 7. C67×#1419 | C2 | semidirect |
| 17. #16863230 | C22 | semidirect |
| 20. #16863226 | C22 | semidirect |
| 23. M64×C67 | C22 | semidirect |
| 24. #368×C67 | C22 | semidirect |
| 125. D67 | #1419 | direct (N × H) |
| 132. #1419 | D67 | direct (N × H) |
| 133. C67 | C2×#1419 | semidirect |
| 146. M64 | C2×D67 | semidirect |
| 150. #368 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D67 | 2 |
| M64×D67 | 2 |
| #368×D67 | 2 |
| #22558400 | 2 |
| #22558399 | 2 |
| #22558398 | 2 |
| C67×#1419 | 2 |
| C2×#1419 | 67 |