Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2520 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 2520 conjugacy classes of subgroups — too many to draw. Only its 744 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C32×C4 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| socle | C23×C32 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C4×D4 | C2 | semidirect |
| 2. C32×#399 | C2 | semidirect |
| 3. C32×#392 | C2 | semidirect |
| 4. C32×#376 | C2 | semidirect |
| 5. C3×#2397 | C3 | direct (N × H) |
| 13. C2×C3×C4×D4 | C2×C3 | semidirect |
| 14. C3×#399 | C2×C3 | semidirect |
| 15. C3×#392 | C2×C3 | semidirect |
| 16. C3×#376 | C2×C3 | semidirect |
| 26. C32×C42 | D4 | semidirect |
| 27. #2397 | C32 | direct (N × H) |
| 45. C2×C4×D4 | C2×C32 | semidirect |
| 46. #399 | C2×C32 | semidirect |
| 47. #392 | C2×C32 | semidirect |
| 48. #376 | C2×C32 | semidirect |
| 58. C3×C42 | C3×D4 | semidirect |
| 96. C42 | C32×D4 | semidirect |
| 105. C32 | #2397 | direct (N × H) |
| 127. C3 | C3×#2397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D4 | 2 |
| C32×#399 | 2 |
| C32×#392 | 2 |
| C32×#376 | 2 |
| C3×#2397 | 3 |