Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
5990 conjugacy classes of subgroups; only the 504 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 504 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#261 |
| commutator, socle | C23×C13 | C23×C4 |
| Fitting, prime radical | C26×C13 | C4 |
| cosocle | C22×Dic13 | C24 |
| hypercenter | C26 | #261 |
| hypocenter | C13 | #20579 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719169 | C2 | semidirect |
| 2. #13130658 | C2 | semidirect |
| 10. C22×#6122 | C22 | semidirect |
| 12. C2×C22⋊#1057 | C22 | semidirect |
| 30. C22×#1057 | C23 | semidirect |
| 40. C24×C13 | M16 | semidirect |
| 104. C22×C13 | #407 | semidirect |
| 139. C24 | #6122 | semidirect |
| 161. C13 | #20579 | semidirect |
| 192. C22 | #11719169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719169 | 2 |
| #13130658 | 2 |
| C25×Dic13 | 2 |
| #20579 | 13 |