Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
63326 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.
This group has 63326 conjugacy classes of subgroups — too many to draw. Only its 34795 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. C24×Dic134 | C2 | semidirect |
| 2. C23×Q8×D67 | C2 | direct (N × H) |
| 4. C24×Q8×C67 | C2 | semidirect |
| 6. C23×Dic134 | C22 | semidirect |
| 7. C22×Q8×D67 | C22 | direct (N × H) |
| 10. C23×Q8×C67 | C22 | semidirect |
| 12. C24×D67 | Q8 | direct (N × H) |
| 14. C22×Dic134 | C23 | semidirect |
| 15. C2×Q8×D67 | C23 | direct (N × H) |
| 19. C22×Q8×C67 | C23 | semidirect |
| 21. C23×D67 | C2×Q8 | direct (N × H) |
| 23. C2×Dic134 | C24 | semidirect |
| 24. Q8×D67 | C24 | direct (N × H) |
| 27. C24×C67 | C2×Q8 | semidirect |
| 29. C2×Q8×C67 | C24 | semidirect |
| 31. C23×C67 | C22×Q8 | semidirect |
| 33. C22×D67 | C22×Q8 | direct (N × H) |
| 35. Q8×C67 | C25 | semidirect |
| 39. Dic134 | C25 | semidirect |
| 40. C22×C67 | C23×Q8 | semidirect |
| 42. C2×D67 | C23×Q8 | direct (N × H) |
| 47. C2×C67 | C24×Q8 | semidirect |
| 49. D67 | C24×Q8 | direct (N × H) |
| 52. C24×Q8 | D67 | direct (N × H) |
| 54. C67 | C25×Q8 | semidirect |
| 58. C23×Q8 | C2×D67 | direct (N × H) |
| 67. C22×Q8 | C22×D67 | direct (N × H) |
| 73. C24 | Q8×D67 | direct (N × H) |
| 77. C2×Q8 | C23×D67 | direct (N × H) |
| 83. C23 | C2×Q8×D67 | direct (N × H) |
| 86. Q8 | C24×D67 | direct (N × H) |
| 92. C22 | C22×Q8×D67 | direct (N × H) |
| 97. C2 | C23×Q8×D67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic134 | 2 |
| C23×Q8×D67 | 2 |
| C24×C4×D67 | 2 |
| C24×Q8×C67 | 2 |
| C25×Q8 | 67 |