Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #447 |
| commutator | C2×C8 | C23×C9 |
| Frattini, cosocle | C2×C3×C8 | C23×C3 |
| socle | C2×C3 | C3×#447 |
| prime radical | C3×#2190 | C3 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C2×C9×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#575 | C2 | semidirect |
| 2. C9×#509 | C2 | semidirect |
| 3. C9×#469 | C2 | semidirect |
| 4. C9×#360 | C2 | semidirect |
| 5. C9×#349 | C2 | semidirect |
| 12. C2×C9×D8 | C22 | semidirect |
| 17. C9×M32 | C22 | semidirect |
| 18. C9×#106 | C22 | semidirect |
| 37. C9×Q16 | D4 | semidirect |
| 42. C9×D8 | D4 | semidirect |
| 49. #2190 | C9 | direct (N × H) |
| 85. #575 | C2×C9 | semidirect |
| 86. #509 | C2×C9 | semidirect |
| 87. #469 | C2×C9 | semidirect |
| 88. #360 | C2×C9 | semidirect |
| 89. #349 | C2×C9 | semidirect |
| 132. C2×D8 | C22×C9 | semidirect |
| 137. M32 | C22×C9 | semidirect |
| 138. #106 | C22×C9 | semidirect |
| 179. Q16 | D4×C9 | semidirect |
| 184. D8 | D4×C9 | semidirect |
| 204. C9 | #2190 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#575 | 2 |
| C9×#509 | 2 |
| C9×#469 | 2 |
| C9×#360 | 2 |
| C9×#349 | 2 |
| C3×#2190 | 3 |