Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
356 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #399 |
| prime radical | C22×D4×C13 | Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#1838 | C2 | semidirect |
| 3. C13×#1571 | C2 | semidirect |
| 4. C13×#1570 | C2 | semidirect |
| 7. C13×#1275 | C2 | semidirect |
| 49. #10659 | C13 | direct (N × H) |
| 82. #1838 | C2×C13 | semidirect |
| 83. #1571 | C2×C13 | semidirect |
| 84. #1570 | C2×C13 | semidirect |
| 87. #1275 | C2×C13 | semidirect |
| 213. C13 | #10659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#1955 | 2 |
| C13×#1838 | 2 |
| C13×#1571 | 2 |
| C13×#1570 | 2 |
| C13×#1486 | 2 |
| C13×#1275 | 2 |
| #10659 | 13 |