Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
552 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C13×C4⋊Q8 | C4 | semidirect |
| 12. C13×#391 | C4 | semidirect |
| 16. C4×C13×C4⋊C4 | C4 | semidirect |
| 53. #13224 | C13 | direct (N × H) |
| 144. C2×C4⋊Q8 | C4×C13 | semidirect |
| 151. #391 | C4×C13 | semidirect |
| 155. C4×C4⋊C4 | C4×C13 | semidirect |
| 186. C4×C13 | #354 | semidirect |
| 270. C13 | #13224 | direct (N × H) |
| 340. C4 | C13×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2547 | 2 |
| C2×C13×#354 | 2 |
| C13×#1799 | 2 |
| C4×C13×#99 | 2 |
| #13224 | 13 |