Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2282 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 2282 conjugacy classes of subgroups — too many to draw. Only its 337 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C3 | C24×A4 |
| commutator, hypocenter | Q8 | C24×C9 |
| Fitting, prime radical | C3×2−1+6 | C3 |
| cosocle | C3×Q8 | C24×C3 |
| hypercenter | C3×H(5,𝔽2) | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C3×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593120 | C2 | semidirect |
| 2. C2×2−1+4⋊C9 | C2 | semidirect |
| 5. 2−1+4⋊C9 | C22 | semidirect |
| 6. #63700 | C22 | semidirect |
| 7. C2×#41⋊C9 | C22 | semidirect |
| 8. C22×Q8⋊C9 | C22 | semidirect |
| 18. 2−1+6 | C9 | semidirect |
| 45. #585 | C2×C9 | semidirect |
| 47. C2×2−1+4 | C2×C9 | semidirect |
| 81. 2−1+4 | C22×C9 | semidirect |
| 86. H(5,𝔽2) | C22×C9 | semidirect |
| 92. C2×#41 | C22×C9 | semidirect |
| 95. C22×Q8 | C22×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593120 | 2 |
| C2×2−1+4⋊C9 | 2 |
| C3×2−1+6 | 3 |
| C9×H(5,𝔽2) | 4 |