Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
528 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 42. #10297 | C13 | direct (N × H) |
| 66. C42×C13 | Q16 | semidirect |
| 166. C42 | C13×Q16 | semidirect |
| 170. C13 | #10297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3209 | 2 |
| C13×#2862 | 2 |
| C13×#1994 | 2 |
| C13×#1548 | 2 |
| C13×#1276 | 2 |
| #10297 | 13 |