Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
5436 conjugacy classes of subgroups; only the 705 normal subgroups are shown.
This group has 5436 conjugacy classes of subgroups — too many to draw. Only its 705 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C23×C3⋊D3 |
| Fitting | C2×C32×#95 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C2×#95 | C3⋊D3 |
| hypocenter | C32 | C2×#392 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C22×#3752 | C2 | semidirect |
| 3. C2×C32×#95 | C2 | semidirect |
| 4. #10592370 | C2 | direct (N × H) |
| 11. C22×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C2×#3752 | C22 | semidirect |
| 14. C32×#95 | C22 | semidirect |
| 17. C2×C3×#95 | D3 | semidirect |
| 24. C23×C3⋊D3 | D4 | semidirect |
| 27. C22×C32×C4 | D4 | semidirect |
| 44. C3×#95 | C2×D3 | semidirect |
| 58. C22×C3⋊D3 | C2×D4 | semidirect |
| 61. C2×C32×C4 | C2×D4 | semidirect |
| 68. C2×#95 | C3⋊D3 | semidirect |
| 77. C22×C3×C4 | D12 | semidirect |
| 107. #95 | C2×C3⋊D3 | semidirect |
| 124. C2×C3×C4 | C2×D12 | semidirect |
| 128. C2×C32 | #392 | semidirect |
| 146. C22×C4 | C4⋊(C3⋊D3) | semidirect |
| 163. C32 | C2×#392 | semidirect |
| 183. C2×C4 | C2×C4⋊(C3⋊D3) | semidirect |
| 184. C2×C3 | #4671 | semidirect |
| 203. C3 | C2×#4671 | semidirect |
| 205. C2 | #10592370 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊(C3⋊D3) | 2 |
| C22×#3752 | 2 |
| C2×C32×#95 | 2 |
| #10592370 | 2 |
| C2×#4671 | 3 |