Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #99 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×D4 | C23×C13 |
| prime radical | C2×C13×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#99 | C2 | semidirect |
| 3. C13×#353 | C2 | direct (N × H) |
| 5. C22×D4×C13 | C4 | semidirect |
| 8. C13×#127 | C4 | semidirect |
| 11. C2×C42×C13 | C4 | semidirect |
| 13. C13×#99 | C22 | semidirect |
| 25. C2×D4×C13 | C2×C4 | semidirect |
| 34. C42×C13 | C2×C4 | semidirect |
| 35. C2×#353 | C13 | direct (N × H) |
| 62. C2×#99 | C2×C13 | semidirect |
| 63. #353 | C2×C13 | direct (N × H) |
| 83. C22×D4 | C4×C13 | semidirect |
| 86. #127 | C4×C13 | semidirect |
| 89. C2×C42 | C4×C13 | semidirect |
| 91. #99 | C22×C13 | semidirect |
| 97. C2×C13 | #353 | direct (N × H) |
| 110. C2×D4 | C2×C4×C13 | semidirect |
| 119. C42 | C2×C4×C13 | semidirect |
| 120. C13 | C2×#353 | direct (N × H) |
| 169. C2 | C13×#353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| C2×C13×#99 | 2 |
| C13×#353 | 2 |
| C2×#353 | 13 |