Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1022 conjugacy classes of subgroups; only the 680 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 680 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #261 |
| commutator, hypocenter | C13 | C22×C4×C16 |
| Frattini | C2×C4 | C23×#261 |
| Fitting | C23×C8×C13 | C4 |
| socle, prime radical | C24×C13 | C2×C8 |
| cosocle | C2×#1055 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#11718257 | C2 | direct (N × H) |
| 7. C22×#6092 | C4 | semidirect |
| 11. #11718257 | C22 | direct (N × H) |
| 21. C2×#6092 | C2×C4 | semidirect |
| 31. C22×Dic13 | C16 | semidirect |
| 41. #6092 | C22×C4 | semidirect |
| 53. C2×Dic13 | C2×C16 | semidirect |
| 66. C22×C13 | C4×C16 | semidirect |
| 73. Dic13 | C22×C16 | semidirect |
| 87. C2×C13 | C2×C4×C16 | semidirect |
| 106. C13 | C22×C4×C16 | semidirect |
| 120. C22 | #11718257 | direct (N × H) |
| 128. C2 | C2×#11718257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6092 | 2 |
| C2×#11718257 | 2 |
| C22×C8×Dic13 | 2 |
| C22×C4×C16 | 13 |