Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
816 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 238 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×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2868 | C2 | semidirect |
| 3. C13×#2043 | C2 | semidirect |
| 5. C13×#1839 | C2 | semidirect |
| 34. #32800 | C13 | direct (N × H) |
| 54. C42×C13 | SD16 | semidirect |
| 55. #2868 | C2×C13 | semidirect |
| 57. #2043 | C2×C13 | semidirect |
| 59. #1839 | C2×C13 | semidirect |
| 141. C42 | C13×SD16 | semidirect |
| 142. C13 | #32800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2868 | 2 |
| C13×#2860 | 2 |
| C13×#2043 | 2 |
| C13×#2013 | 2 |
| C13×#1839 | 2 |
| #32800 | 13 |