Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1598 |
| commutator, Frattini, cosocle | C2×M16 | C23×C13 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#3255 | C2 | semidirect |
| 4. C13×#1342 | C2 | semidirect |
| 5. C13×#1327 | C2 | semidirect |
| 49. #12174 | C13 | direct (N × H) |
| 86. #3255 | C2×C13 | semidirect |
| 89. #1342 | C2×C13 | semidirect |
| 90. #1327 | C2×C13 | semidirect |
| 213. C13 | #12174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3255 | 2 |
| C13×#2191 | 2 |
| C13×#2050 | 2 |
| C13×#1342 | 2 |
| C13×#1327 | 2 |
| #12174 | 13 |