Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
231 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C9 | #459 |
| commutator | C2×C8 | C23×C9 |
| Frattini, cosocle | C2×C3×C8 | C23×C3 |
| socle | C2×C3 | C3×#459 |
| prime radical | C3×#509 | C2×C3 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C4×C8×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#510 | C2 | semidirect |
| 3. C9×#495 | C2 | semidirect |
| 4. C9×#443 | C2 | semidirect |
| 5. C9×#364 | C2 | semidirect |
| 6. C9×#362 | C2 | semidirect |
| 7. C9×#361 | C2 | semidirect |
| 52. #2212 | C9 | direct (N × H) |
| 85. #510 | C2×C9 | semidirect |
| 87. #495 | C2×C9 | semidirect |
| 88. #443 | C2×C9 | semidirect |
| 89. #364 | C2×C9 | semidirect |
| 90. #362 | C2×C9 | semidirect |
| 91. #361 | C2×C9 | semidirect |
| 188. C9 | #2212 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#510 | 2 |
| C9×#509 | 2 |
| C9×#495 | 2 |
| C9×#443 | 2 |
| C9×#364 | 2 |
| C9×#362 | 2 |
| C9×#361 | 2 |
| C3×#2212 | 3 |