Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | C2×D8 |
| commutator | C2×C8 | C23×C9 |
| Frattini, cosocle | C2×C3×C8 | C23×C3 |
| socle | C22×C3 | C2×C3×D8 |
| prime radical | C23×C3 | C3×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C22×C8×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C9×Q32 | C2 | semidirect |
| 4. C9×#358 | C2 | semidirect |
| 41. #2188 | C9 | direct (N × H) |
| 70. C2×Q32 | C2×C9 | semidirect |
| 72. #358 | C2×C9 | semidirect |
| 94. C22×C9 | Q32 | semidirect |
| 161. C9 | #2188 | direct (N × H) |
| 184. C22 | C9×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Q16 | 2 |
| C2×C9×Q32 | 2 |
| C9×#467 | 2 |
| C9×#358 | 2 |
| C9×C22⋊C16 | 2 |
| C3×#2188 | 3 |