Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
936 conjugacy classes of subgroups; only the 540 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 540 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24×C9 | C23 |
| commutator | C22 | C23×C4×C9 |
| Frattini, cosocle | C23×C3 | C24×C3 |
| socle, prime radical | C24×C3 | C23×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#383 | C2 | direct (N × H) |
| 7. C2×C42×C9 | C4 | semidirect |
| 19. C42×C9 | C2×C4 | semidirect |
| 20. C2×#383 | C9 | direct (N × H) |
| 35. #383 | C2×C9 | direct (N × H) |
| 52. C2×C42 | C4×C9 | semidirect |
| 63. C2×C9 | #383 | direct (N × H) |
| 72. C42 | C2×C4×C9 | semidirect |
| 79. C9 | C2×#383 | direct (N × H) |
| 98. C2 | C9×#383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C9 | 2 |
| C9×#383 | 2 |
| C2×C9×#95 | 2 |
| C2×C3×#383 | 3 |