Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
292 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D4 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| socle | C22×C13 | C4×D4 |
| prime radical | C2×C13×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#108 | C2 | semidirect |
| 3. C2×C13×#104 | C2 | semidirect |
| 4. C13×#408 | C2 | semidirect |
| 5. C2×C13×#97 | C2 | semidirect |
| 9. C2×C13×Q16 | C4 | semidirect |
| 10. C2×C13×SD16 | C4 | semidirect |
| 11. C2×C13×D8 | C4 | semidirect |
| 45. #1975 | C13 | direct (N × H) |
| 70. C2×#108 | C2×C13 | semidirect |
| 71. C2×#104 | C2×C13 | semidirect |
| 72. #408 | C2×C13 | semidirect |
| 73. C2×#97 | C2×C13 | semidirect |
| 89. C2×Q16 | C4×C13 | semidirect |
| 90. C2×SD16 | C4×C13 | semidirect |
| 91. C2×D8 | C4×C13 | semidirect |
| 130. C13 | #1975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| C2×C13×#108 | 2 |
| C2×C13×#104 | 2 |
| C13×#408 | 2 |
| C2×C13×#97 | 2 |
| #1975 | 13 |