Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
270 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #261 |
| commutator, hypocenter | C13 | C2×C4×C32 |
| Frattini | C16 | C22×#261 |
| Fitting | C2×C13×C32 | C4 |
| socle | C22×C13 | C4×C16 |
| prime radical | C22×D13 | C2×C16 |
| cosocle | C16×D13 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#261 | C2 | direct (N × H) |
| 8. C2×#88036 | C4 | semidirect |
| 11. D13⋊C32 | C4 | semidirect |
| 13. C2×C13×C32 | C4 | semidirect |
| 14. C2×#88034 | C4 | semidirect |
| 15. D13×C32 | C4 | semidirect |
| 31. #88036 | C2×C4 | semidirect |
| 32. C13×C32 | C2×C4 | semidirect |
| 33. #88034 | C2×C4 | semidirect |
| 58. C2×#261 | C32 | direct (N × H) |
| 80. C2×C32 | #261 | direct (N × H) |
| 87. #261 | C2×C32 | direct (N × H) |
| 108. C32 | C2×#261 | direct (N × H) |
| 109. C2×C13 | C4×C32 | semidirect |
| 111. D13 | C4×C32 | semidirect |
| 131. C13 | C2×C4×C32 | semidirect |
| 157. C2 | C32×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13⋊C32 | 2 |
| C2×C16×#261 | 2 |
| C32×#261 | 2 |
| C2×D13×C32 | 2 |
| C2×C4×C32 | 13 |