Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1092 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 222 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| prime radical | C2×C13×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#563 | C2 | semidirect |
| 2. C2×C13×#456 | C2 | semidirect |
| 4. C13×#2203 | C2 | direct (N × H) |
| 5. C2×C13×#356 | C2 | semidirect |
| 6. C2×C13×#355 | C2 | semidirect |
| 12. C13×#563 | C22 | semidirect |
| 20. C13×#456 | C22 | semidirect |
| 27. C13×#356 | C22 | semidirect |
| 28. C13×#355 | C22 | semidirect |
| 82. C2×#2203 | C13 | direct (N × H) |
| 151. C2×#563 | C2×C13 | semidirect |
| 152. C2×#456 | C2×C13 | semidirect |
| 154. #2203 | C2×C13 | direct (N × H) |
| 155. C2×#356 | C2×C13 | semidirect |
| 156. C2×#355 | C2×C13 | semidirect |
| 208. #563 | C22×C13 | semidirect |
| 216. #456 | C22×C13 | semidirect |
| 223. #356 | C22×C13 | semidirect |
| 224. #355 | C22×C13 | semidirect |
| 300. C2×C13 | #2203 | direct (N × H) |
| 370. C13 | C2×#2203 | direct (N × H) |
| 439. C2 | C13×#2203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#563 | 2 |
| C2×C13×#456 | 2 |
| C2×C13×#454 | 2 |
| C13×#2203 | 2 |
| C2×C13×#356 | 2 |
| C2×C13×#355 | 2 |
| C2×#2203 | 13 |