Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1968 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 337 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×C32×#127 | C2 | semidirect |
| 2. C2×#64141 | C2 | semidirect |
| 3. #10595948 | C2 | semidirect |
| 4. #10592775 | C2 | semidirect |
| 5. #10592773 | C2 | semidirect |
| 6. #10592772 | C2 | semidirect |
| 7. C4×#3748 | C2 | semidirect |
| 16. C2×#3754 | C22 | semidirect |
| 18. C2×#3753 | C22 | semidirect |
| 21. #64084 | C22 | semidirect |
| 22. #64083 | C22 | semidirect |
| 24. #64078 | C22 | semidirect |
| 25. #63630 | C22 | semidirect |
| 26. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 27. C2×C3×#127 | D3 | semidirect |
| 56. #3748 | D4 | semidirect |
| 98. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 101. C2×#127 | C3⋊D3 | semidirect |
| 140. C32×C4 | AGL(1,ℤ/8) | semidirect |
| 221. C3×C4 | #932 | semidirect |
| 225. C32 | #3151 | semidirect |
| 263. C4 | #64141 | semidirect |
| 266. C3 | #83163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C2×#64141 | 2 |
| #10595948 | 2 |
| #10592775 | 2 |
| #10592773 | 2 |
| #10592772 | 2 |
| C4×#3748 | 2 |
| #83163 | 3 |