Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1944 conjugacy classes of subgroups; only the 792 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 792 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator | C22 | C23×C32×C4 |
| Frattini, cosocle | C23 | C24×C32 |
| prime radical | C2×C32×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#386 | C2 | semidirect |
| 3. C32×#383 | C2 | semidirect |
| 4. C3×#2380 | C3 | direct (N × H) |
| 7. C32×#127 | C4 | semidirect |
| 12. C3×#386 | C2×C3 | semidirect |
| 13. C3×#383 | C2×C3 | semidirect |
| 17. C2×C32×D4 | C2×C4 | semidirect |
| 22. C32×C42 | C2×C4 | semidirect |
| 23. #2380 | C32 | direct (N × H) |
| 26. C3×#127 | C3×C4 | semidirect |
| 40. #386 | C2×C32 | semidirect |
| 41. #383 | C2×C32 | semidirect |
| 45. C2×C3×D4 | C2×C3×C4 | semidirect |
| 50. C3×C42 | C2×C3×C4 | semidirect |
| 60. #127 | C32×C4 | semidirect |
| 79. C2×D4 | C2×C32×C4 | semidirect |
| 84. C42 | C2×C32×C4 | semidirect |
| 92. C32 | #2380 | direct (N × H) |
| 112. C3 | C3×#2380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C32×#386 | 2 |
| C32×#383 | 2 |
| C3×#2380 | 3 |