Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2832 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 2832 conjugacy classes of subgroups — too many to draw. Only its 339 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#395 | C2 |
| hypercenter | #395 | C3⋊D3 |
| hypocenter | C32 | #2388 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3832 | C2 | semidirect |
| 2. C2×#64102 | C2 | semidirect |
| 3. C32×#395 | C2 | semidirect |
| 4. #10592930 | C2 | semidirect |
| 5. #10592690 | C2 | semidirect |
| 6. #10592370 | C2 | semidirect |
| 7. #10592365 | C2 | semidirect |
| 25. C3×#395 | D3 | semidirect |
| 46. C2×C4×C3⋊D3 | D4 | semidirect |
| 75. C22×C3⋊D3 | #41 | semidirect |
| 82. C2×C32×C4 | #41 | semidirect |
| 92. #395 | C3⋊D3 | semidirect |
| 164. C2×C3×C4 | #239 | semidirect |
| 215. C32 | #2388 | semidirect |
| 238. C2×C4 | #3832 | semidirect |
| 260. C3 | #77169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C2×#64102 | 2 |
| C32×#395 | 2 |
| #10592930 | 2 |
| #10592690 | 2 |
| #10592370 | 2 |
| #10592365 | 2 |
| #77169 | 3 |