Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1752 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 1752 conjugacy classes of subgroups — too many to draw. Only its 600 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| prime radical | C2×C32×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C32×#125 | C2 | semidirect |
| 3. C32×#394 | C2 | semidirect |
| 4. C32×#390 | C2 | semidirect |
| 5. C32×#376 | C2 | semidirect |
| 6. C3×#2641 | C3 | direct (N × H) |
| 18. C2×C3×#125 | C2×C3 | semidirect |
| 19. C3×#394 | C2×C3 | semidirect |
| 20. C3×#390 | C2×C3 | semidirect |
| 21. C3×#376 | C2×C3 | semidirect |
| 36. #2641 | C32 | direct (N × H) |
| 62. C2×#125 | C2×C32 | semidirect |
| 63. #394 | C2×C32 | semidirect |
| 64. #390 | C2×C32 | semidirect |
| 65. #376 | C2×C32 | semidirect |
| 142. C32 | #2641 | direct (N × H) |
| 171. C3 | C3×#2641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C2×C32×#125 | 2 |
| C32×#394 | 2 |
| C32×#390 | 2 |
| C32×#376 | 2 |
| C3×#2641 | 3 |