Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1074 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 318 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 | C2×#120 |
| commutator | C23 | C24×C9 |
| Frattini, cosocle | C23×C3 | C24×C3 |
| socle | C2×C3 | C2×C3×#120 |
| prime radical | C3×#585 | C2×C3 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#536 | C2 | semidirect |
| 3. C9×#458 | C2 | semidirect |
| 4. C9×#410 | C2 | semidirect |
| 11. C22×Q8×C9 | C22 | semidirect |
| 14. C9×#123 | C22 | semidirect |
| 16. C9×#117 | C22 | semidirect |
| 17. C9×#99 | C22 | semidirect |
| 44. #3028 | C9 | direct (N × H) |
| 76. #536 | C2×C9 | semidirect |
| 77. #458 | C2×C9 | semidirect |
| 78. #410 | C2×C9 | semidirect |
| 116. C22×Q8 | C22×C9 | semidirect |
| 119. #123 | C22×C9 | semidirect |
| 121. #117 | C22×C9 | semidirect |
| 122. #99 | C22×C9 | semidirect |
| 176. C9 | #3028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#585 | 2 |
| C9×#536 | 2 |
| C9×#458 | 2 |
| C9×#410 | 2 |
| C3×#3028 | 3 |