Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
556 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×#261 |
| commutator, socle | C22×C13 | C23×C8 |
| Fitting, prime radical | C13×#532 | C4 |
| cosocle | C2×#1055 | C24 |
| hypercenter | #532 | #261 |
| hypocenter | C13 | #33494 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131216 | C2 | semidirect |
| 2. #13131197 | C2 | semidirect |
| 3. #13131066 | C2 | semidirect |
| 163. C13 | #33494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131216 | 2 |
| #13131197 | 2 |
| #13131066 | 2 |
| #13123548 | 2 |
| #33494 | 13 |