Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 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. #1009 | C2 | semidirect |
| 2. C3×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #940 | C2 | semidirect |
| 4. #932 | C2 | semidirect |
| 5. #837 | C2 | semidirect |
| 6. #825 | C2 | semidirect |
| 7. #823 | C2 | semidirect |
| 10. C2×C3×D4 | C22 | semidirect |
| 21. C3×M16 | C22 | semidirect |
| 24. C4×Dic3 | C22 | semidirect |
| 25. #208 | C22 | semidirect |
| 28. AGL(1,ℤ/8) | D3 | semidirect |
| 36. C3×Q8 | D4 | semidirect |
| 40. C3×D4 | D4 | semidirect |
| 50. D12 | D4 | semidirect |
| 53. Dic6 | D4 | semidirect |
| 65. C2×D4 | C2×D3 | semidirect |
| 71. M16 | C2×D3 | semidirect |
| 90. Q8 | #67 | semidirect |
| 101. D4 | #67 | semidirect |
| 128. C3 | #453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1009 | 2 |
| C3×AGL(1,ℤ/8) | 2 |
| #940 | 2 |
| #932 | 2 |
| #837 | 2 |
| #825 | 2 |
| #823 | 2 |
| #453 | 3 |