Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
220 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C8 | C22×C4×C13 |
| Frattini, cosocle | C2×C8 | C23×C13 |
| prime radical | C23×C13 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C13×#358 | C2 | semidirect |
| 8. C2×C13×Q16 | C4 | semidirect |
| 33. #2141 | C13 | direct (N × H) |
| 51. #358 | C2×C13 | semidirect |
| 63. C2×Q16 | C4×C13 | semidirect |
| 91. C13 | #2141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C2×C13×M32 | 2 |
| C13×#427 | 2 |
| C13×#358 | 2 |
| #2141 | 13 |