Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
324 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1514 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C2×M16 | C23×C13 |
| prime radical | C13×#3184 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2165 | C2 | semidirect |
| 3. C13×#1841 | C2 | semidirect |
| 4. C13×#1341 | C2 | semidirect |
| 5. C13×#1339 | C2 | semidirect |
| 7. C13×#498 | C4 | semidirect |
| 8. C13×#493 | C4 | semidirect |
| 13. C13×#442 | C4 | semidirect |
| 46. #11837 | C13 | direct (N × H) |
| 79. #2165 | C2×C13 | semidirect |
| 80. #1841 | C2×C13 | semidirect |
| 81. #1341 | C2×C13 | semidirect |
| 82. #1339 | C2×C13 | semidirect |
| 107. #498 | C4×C13 | semidirect |
| 108. #493 | C4×C13 | semidirect |
| 113. #442 | C4×C13 | semidirect |
| 194. C13 | #11837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3184 | 2 |
| C13×#2165 | 2 |
| C13×#1841 | 2 |
| C13×#1341 | 2 |
| C13×#1339 | 2 |
| #11837 | 13 |