Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 84 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 | B(4,𝔽2) |
| commutator | C2×Q8 | C23×C9 |
| Frattini, cosocle | C2×C3×Q8 | C23×C3 |
| socle | C2×C3 | C3×B(4,𝔽2) |
| prime radical | C3×2−1+4 | C22×C3 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C22×C9 ◁ C2×Q8×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q82×C9 | C2 | semidirect |
| 3. C9×#356 | C2 | semidirect |
| 29. #2205 | C9 | direct (N × H) |
| 49. Q82 | C2×C9 | semidirect |
| 51. #356 | C2×C9 | semidirect |
| 114. C9 | #2205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C9 | 2 |
| C9×#456 | 2 |
| C9×#356 | 2 |
| C3×#2205 | 3 |