Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
600 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2101 | C2 | semidirect |
| 4. C13×#2058 | C2 | semidirect |
| 40. #32794 | C13 | direct (N × H) |
| 64. #2101 | C2×C13 | semidirect |
| 66. #2058 | C2×C13 | semidirect |
| 161. C13 | #32794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2628 | 2 |
| C13×#2101 | 2 |
| C13×#2077 | 2 |
| C13×#2058 | 2 |
| C13×#1818 | 2 |
| #32794 | 13 |