Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
112 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C2×C4×C13 |
| Frattini, cosocle | #124 | C22×C13 |
| prime radical | C13×H(5,𝔽2) | C4 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C13 ◁ C2×C4×C13 ◁ C13×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#355 | C2 | semidirect |
| 3. C13×#329 | C2 | semidirect |
| 24. #1403 | C13 | direct (N × H) |
| 42. #355 | C2×C13 | semidirect |
| 43. #329 | C2×C13 | semidirect |
| 77. C13 | #1403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#455 | 2 |
| C13×#355 | 2 |
| C13×#329 | 2 |
| #1403 | 13 |