Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 226 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. C32×C82 | C2 | semidirect |
| 3. C3×#4455 | C2 | semidirect |
| 5. #68050 | C3 | direct (N × H) |
| 15. C3×C82 | D3 | semidirect |
| 16. C3×C82 | C2×C3 | semidirect |
| 17. #4455 | C2×C3 | semidirect |
| 40. C32×C8 | M16 | semidirect |
| 44. C82 | C3×D3 | semidirect |
| 79. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 80. C3×C8 | C3×M16 | semidirect |
| 100. C32 | #1455 | semidirect |
| 106. C8 | C3×ΓL(1,𝔽25) | semidirect |
| 117. C3 | #68050 | direct (N × H) |
| 118. C3 | C3×#1455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×ΓL(1,𝔽25) | 2 |
| C32×C82 | 2 |
| C3×#4455 | 2 |
| C3×#1455 | 3 |
| #68050 | 3 |