Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
786 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C24×C13 ◁ C23×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C13×#1393 | C2 | semidirect |
| 5. C2×C13×#117 | C4 | semidirect |
| 6. C2×C13×#117 | C4 | semidirect |
| 10. C13×#390 | C4 | semidirect |
| 36. #12858 | C13 | direct (N × H) |
| 75. #1393 | C2×C13 | semidirect |
| 112. C2×#117 | C4×C13 | semidirect |
| 113. C2×#117 | C4×C13 | semidirect |
| 117. #390 | C4×C13 | semidirect |
| 208. C13 | #12858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2309 | 2 |
| C13×#1781 | 2 |
| C13×#1393 | 2 |
| #12858 | 13 |