Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 630 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 | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C13×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2644 | C2 | semidirect |
| 2. C13×#2087 | C2 | semidirect |
| 3. C13×#2067 | C2 | semidirect |
| 5. C13×#1843 | C2 | semidirect |
| 34. #32867 | C13 | direct (N × H) |
| 53. #2644 | C2×C13 | semidirect |
| 54. #2087 | C2×C13 | semidirect |
| 55. #2067 | C2×C13 | semidirect |
| 57. #1843 | C2×C13 | semidirect |
| 137. C13 | #32867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2644 | 2 |
| C13×#2087 | 2 |
| C13×#2067 | 2 |
| C13×#2054 | 2 |
| C13×#1843 | 2 |
| #32867 | 13 |