Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
426 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#427 | C2 | semidirect |
| 3. C32×#367 | C2 | semidirect |
| 4. C32×#366 | C2 | semidirect |
| 5. C32×#357 | C2 | semidirect |
| 6. C32×#357 | C2 | semidirect |
| 7. C32×C22⋊C16 | C2 | semidirect |
| 8. C3×#2234 | C3 | direct (N × H) |
| 21. C3×#427 | C2×C3 | semidirect |
| 22. C3×#367 | C2×C3 | semidirect |
| 23. C3×#366 | C2×C3 | semidirect |
| 24. C3×#357 | C2×C3 | semidirect |
| 25. C3×#357 | C2×C3 | semidirect |
| 26. C3×C22⋊C16 | C2×C3 | semidirect |
| 44. #2234 | C32 | direct (N × H) |
| 72. #427 | C2×C32 | semidirect |
| 73. #367 | C2×C32 | semidirect |
| 74. #366 | C2×C32 | semidirect |
| 75. #357 | C2×C32 | semidirect |
| 76. #357 | C2×C32 | semidirect |
| 77. C22⋊C16 | C2×C32 | semidirect |
| 169. C32 | #2234 | direct (N × H) |
| 203. C3 | C3×#2234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#466 | 2 |
| C32×#427 | 2 |
| C32×#367 | 2 |
| C32×#366 | 2 |
| C32×#357 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#2234 | 3 |