Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
412 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#125 | C2 | semidirect |
| 3. C13×#488 | C2 | direct (N × H) |
| 4. C2×C13×#103 | C2 | semidirect |
| 6. C2×C4×C8×C13 | C2 | semidirect |
| 11. C13×#125 | C22 | semidirect |
| 18. C13×#103 | C22 | semidirect |
| 20. C4×C8×C13 | C22 | semidirect |
| 40. C2×#488 | C13 | direct (N × H) |
| 59. C2×#125 | C2×C13 | semidirect |
| 61. #488 | C2×C13 | direct (N × H) |
| 62. C2×#103 | C2×C13 | semidirect |
| 64. C2×C4×C8 | C2×C13 | semidirect |
| 80. #125 | C22×C13 | semidirect |
| 87. #103 | C22×C13 | semidirect |
| 89. C4×C8 | C22×C13 | semidirect |
| 91. C2×C13 | #488 | direct (N × H) |
| 113. C13 | C2×#488 | direct (N × H) |
| 144. C2 | C13×#488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#125 | 2 |
| C2×C13×#124 | 2 |
| C13×#488 | 2 |
| C2×C13×#103 | 2 |
| C2×C13×#102 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#488 | 13 |