Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C2×C32×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#510 | C2 | semidirect |
| 3. C32×#470 | C2 | semidirect |
| 4. C32×#360 | C2 | semidirect |
| 5. C32×#349 | C2 | semidirect |
| 6. C3×#2191 | C3 | direct (N × H) |
| 12. C2×C32×Q16 | C22 | semidirect |
| 17. C32×M32 | C22 | semidirect |
| 18. C32×#106 | C22 | semidirect |
| 21. C3×#510 | C2×C3 | semidirect |
| 22. C3×#470 | C2×C3 | semidirect |
| 23. C3×#360 | C2×C3 | semidirect |
| 24. C3×#349 | C2×C3 | semidirect |
| 49. #2191 | C32 | direct (N × H) |
| 55. C2×C3×Q16 | C22×C3 | semidirect |
| 60. C3×M32 | C22×C3 | semidirect |
| 61. C3×#106 | C22×C3 | semidirect |
| 85. #510 | C2×C32 | semidirect |
| 86. #470 | C2×C32 | semidirect |
| 87. #360 | C2×C32 | semidirect |
| 88. #349 | C2×C32 | semidirect |
| 129. C2×Q16 | C22×C32 | semidirect |
| 134. M32 | C22×C32 | semidirect |
| 135. #106 | C22×C32 | semidirect |
| 197. C32 | #2191 | direct (N × H) |
| 234. C3 | C3×#2191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| C32×#510 | 2 |
| C32×#470 | 2 |
| C32×#360 | 2 |
| C32×#349 | 2 |
| C3×#2191 | 3 |