Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | #120 |
| commutator | C24 | C23×C9 |
| Frattini, cosocle | C24×C3 | C23×C3 |
| socle | C22×C3 | C3×#120 |
| prime radical | C3×#534 | C2×C3 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C24×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C9×#99 | C2 | semidirect |
| 3. C9×#386 | C2 | semidirect |
| 4. C9×#385 | C2 | semidirect |
| 5. C9×#342 | C2 | semidirect |
| 54. C9×C22⋊C4 | D4 | semidirect |
| 55. #2044 | C9 | direct (N × H) |
| 107. C2×#99 | C2×C9 | semidirect |
| 108. #386 | C2×C9 | semidirect |
| 109. #385 | C2×C9 | semidirect |
| 110. #342 | C2×C9 | semidirect |
| 249. C22⋊C4 | D4×C9 | semidirect |
| 273. C9 | #2044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#534 | 2 |
| C2×C9×#99 | 2 |
| C9×#386 | 2 |
| C9×#385 | 2 |
| C9×#342 | 2 |
| C3×#2044 | 3 |