Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
556 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2804 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2102 | C2 | semidirect |
| 2. C13×#2031 | C2 | semidirect |
| 3. C13×#1994 | C2 | semidirect |
| 6. C13×#1861 | C2 | semidirect |
| 27. C13×C4⋊Q8 | Q8 | semidirect |
| 28. C13×#127 | Q8 | semidirect |
| 30. C13×#124 | Q8 | semidirect |
| 46. #32704 | C13 | direct (N × H) |
| 79. #2102 | C2×C13 | semidirect |
| 80. #2031 | C2×C13 | semidirect |
| 81. #1994 | C2×C13 | semidirect |
| 84. #1861 | C2×C13 | semidirect |
| 142. C4⋊Q8 | Q8×C13 | semidirect |
| 143. #127 | Q8×C13 | semidirect |
| 145. #124 | Q8×C13 | semidirect |
| 197. C13 | #32704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2102 | 2 |
| C13×#2031 | 2 |
| C13×#1994 | 2 |
| C13×#1962 | 2 |
| C13×#1884 | 2 |
| C13×#1861 | 2 |
| #32704 | 13 |