Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 516 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 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2921 | C2 | semidirect |
| 3. C13×#1820 | C2 | semidirect |
| 5. C13×#1284 | C2 | semidirect |
| 14. C13×#390 | C4 | semidirect |
| 15. C13×#390 | C4 | semidirect |
| 18. C13×#384 | C4 | semidirect |
| 19. C13×#382 | C4 | semidirect |
| 61. #9446 | C13 | direct (N × H) |
| 109. #2921 | C2×C13 | semidirect |
| 111. #1820 | C2×C13 | semidirect |
| 113. #1284 | C2×C13 | semidirect |
| 167. #390 | C4×C13 | semidirect |
| 168. #390 | C4×C13 | semidirect |
| 171. #384 | C4×C13 | semidirect |
| 172. #382 | C4×C13 | semidirect |
| 296. C13 | #9446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2921 | 2 |
| C13×#2500 | 2 |
| C13×#1820 | 2 |
| C13×#1510 | 2 |
| C13×#1284 | 2 |
| #9446 | 13 |