Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
558 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | #261 |
| commutator, hypocenter | C13 | C42×C16 |
| Frattini | C22×C4 | C22×#261 |
| Fitting | C2×C4×C8×C13 | C4 |
| socle, prime radical | C23×C13 | C22×C8 |
| cosocle | C22×#1055 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #11718257 | C4 | direct (N × H) |
| 11. C4×#6092 | C4 | semidirect |
| 33. C4×Dic13 | C16 | semidirect |
| 40. #6092 | C42 | semidirect |
| 67. C4×C13 | C4×C16 | semidirect |
| 71. Dic13 | C4×C16 | semidirect |
| 103. C13 | C42×C16 | semidirect |
| 120. C4 | #11718257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718257 | 2 |
| C2×C4×#6092 | 2 |
| C4×C8×Dic13 | 2 |
| C42×C16 | 13 |