Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C13 |
| prime radical | C2×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ C4×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#499 | C2 | semidirect |
| 3. C13×#358 | C2 | semidirect |
| 5. C4×C13×C16 | C2 | semidirect |
| 27. #2242 | C13 | direct (N × H) |
| 39. #499 | C2×C13 | semidirect |
| 41. #358 | C2×C13 | semidirect |
| 43. C4×C16 | C2×C13 | semidirect |
| 76. C13 | #2242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#499 | 2 |
| C13×#495 | 2 |
| C13×#358 | 2 |
| C13×#357 | 2 |
| C4×C13×C16 | 2 |
| #2242 | 13 |