Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
900 conjugacy classes of subgroups; only the 624 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 624 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C32×C4 | C23 |
| commutator | C22 | C22×C32×C8 |
| Frattini, cosocle | C22×C4 | C23×C32 |
| socle, prime radical | C23×C32 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#1842 | C3 | direct (N × H) |
| 16. C32×C42 | C8 | semidirect |
| 19. #1842 | C32 | direct (N × H) |
| 41. C3×C42 | C3×C8 | semidirect |
| 48. C32×C4 | C4⋊C8 | semidirect |
| 73. C42 | C32×C8 | semidirect |
| 80. C3×C4 | C3×C4⋊C8 | semidirect |
| 83. C32 | #1842 | direct (N × H) |
| 100. C4 | C32×C4⋊C8 | semidirect |
| 103. C3 | C3×#1842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊C8 | 2 |
| C32×C43 | 2 |
| C3×#1842 | 3 |