Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2208 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 2208 conjugacy classes of subgroups — too many to draw. Only its 744 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C32 | C23 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C24 | C23×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#1446 | C3 | direct (N × H) |
| 5. C22×C32×Q8 | C4 | semidirect |
| 19. C22×C32×C4 | Q8 | semidirect |
| 20. #1446 | C32 | direct (N × H) |
| 22. C22×C3×Q8 | C3×C4 | semidirect |
| 47. C22×C3×C4 | C3×Q8 | semidirect |
| 57. C22×Q8 | C32×C4 | semidirect |
| 84. C22×C4 | C32×Q8 | semidirect |
| 93. C32 | #1446 | direct (N × H) |
| 117. C3 | C3×#1446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C2×C32×#95 | 2 |
| C3×#1446 | 3 |