Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#41×C29 | C2 | semidirect |
| 2. C22×D116 | C2 | semidirect |
| 3. #11745311 | C2 | direct (N × H) |
| 4. C2×#90784 | C2 | semidirect |
| 5. C2×#90782 | C2 | semidirect |
| 6. C2×#90777 | C2 | semidirect |
| 9. #41×C29 | C22 | semidirect |
| 10. C2×Q8×C29 | C22 | semidirect |
| 12. C2×D4×C29 | C22 | semidirect |
| 18. C2×D116 | C22 | semidirect |
| 19. #90784 | C22 | semidirect |
| 20. #90782 | C22 | semidirect |
| 21. #90777 | C22 | semidirect |
| 22. C2×#6597 | C22 | semidirect |
| 29. Q8×C29 | C23 | semidirect |
| 32. D4×C29 | C23 | semidirect |
| 42. #6597 | C23 | semidirect |
| 58. C2×C29 | AGL(1,ℤ/8) | semidirect |
| 61. C2×#41 | D29 | semidirect |
| 67. C29 | C2×AGL(1,ℤ/8) | semidirect |
| 70. #41 | C2×D29 | semidirect |
| 71. C2×Q8 | C2×D29 | semidirect |
| 77. C2×D4 | C2×D29 | semidirect |
| 90. Q8 | C22×D29 | semidirect |
| 96. D4 | C22×D29 | semidirect |
| 119. C2 | #11745311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C29 | 2 |
| C22×D116 | 2 |
| #11745311 | 2 |
| C2×#90784 | 2 |
| C2×#90782 | 2 |
| C2×#90777 | 2 |
| C2×AGL(1,ℤ/8) | 29 |