Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
6249 conjugacy classes of subgroups; only the 1012 normal subgroups are shown.
This group has 6249 conjugacy classes of subgroups — too many to draw. Only its 1012 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C23×C32×C4 | C22 |
| socle | C24×C32 | C23 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | C22×#127 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C3×D12 | C2 | semidirect |
| 2. C23×#625 | C2 | semidirect |
| 3. C22×C4×C3⋊Dic3 | C2 | semidirect |
| 4. C2×#63914 | C2 | direct (N × H) |
| 10. C22×C3×D12 | C22 | semidirect |
| 12. C22×#625 | C22 | semidirect |
| 13. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 14. #63914 | C22 | direct (N × H) |
| 17. C23×D12 | D3 | semidirect |
| 25. C22×C32×C4 | D4 | semidirect |
| 27. C22×C3⋊Dic3 | D4 | semidirect |
| 30. C2×C3×D12 | C23 | semidirect |
| 32. C2×#625 | C23 | semidirect |
| 33. C4×C3⋊Dic3 | C23 | semidirect |
| 46. C22×D12 | C2×D3 | semidirect |
| 57. C2×C32×C4 | C2×D4 | semidirect |
| 59. C2×C3⋊Dic3 | C2×D4 | semidirect |
| 79. C22×C3×C4 | #67 | semidirect |
| 88. C2×D12 | C22×D3 | semidirect |
| 91. C22×C32 | #127 | semidirect |
| 98. C32×C4 | C22×D4 | semidirect |
| 99. C3⋊Dic3 | C22×D4 | semidirect |
| 126. C2×C3×C4 | C2×#67 | semidirect |
| 134. C2×C32 | C2×#127 | semidirect |
| 148. C22×C4 | #625 | semidirect |
| 158. C22×C3 | #940 | semidirect |
| 166. C3×C4 | C22×#67 | semidirect |
| 169. C32 | C22×#127 | semidirect |
| 181. C2×C4 | C2×#625 | semidirect |
| 187. C2×C3 | C2×#940 | semidirect |
| 194. C22 | #63914 | direct (N × H) |
| 199. C4 | C22×#625 | semidirect |
| 201. C3 | C22×#940 | semidirect |
| 203. C2 | C2×#63914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D12 | 2 |
| C23×#625 | 2 |
| C22×C4×C3⋊Dic3 | 2 |
| C2×#63914 | 2 |
| C22×#940 | 3 |