Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #261 |
| commutator, hypocenter | C13 | C22×C4×C8 |
| Frattini | C22 | C23×#261 |
| Fitting | C2×C42×C13 | C4 |
| socle | C23×C13 | C22×C4 |
| prime radical | C23×D13 | C2×C4 |
| cosocle | C2×Dic13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×#1057 | C2 | semidirect |
| 4. C4×D13⋊C8 | C2 | direct (N × H) |
| 8. C2×D13⋊C8 | C4 | direct (N × H) |
| 15. C4×#1057 | C22 | semidirect |
| 21. C2×C4×D13 | C8 | semidirect |
| 26. C2×#1057 | C2×C4 | semidirect |
| 28. D13⋊C8 | C2×C4 | direct (N × H) |
| 39. C2×C4×C13 | C2×C8 | semidirect |
| 42. C2×Dic13 | C2×C8 | semidirect |
| 48. C4×D13 | C2×C8 | semidirect |
| 50. #1057 | C22×C4 | semidirect |
| 58. C2×D13 | C4×C8 | semidirect |
| 62. C4×C13 | C22×C8 | semidirect |
| 64. Dic13 | C22×C8 | semidirect |
| 77. C2×C13 | C2×C4×C8 | semidirect |
| 80. D13 | C2×C4×C8 | semidirect |
| 98. C13 | C22×C4×C8 | semidirect |
| 111. C2×C4 | D13⋊C8 | direct (N × H) |
| 125. C4 | C2×D13⋊C8 | direct (N × H) |
| 128. C2 | C4×D13⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D13⋊C8 | 2 |
| C2×C42×D13 | 2 |
| C2×C4×#1057 | 2 |
| C4×D13⋊C8 | 2 |
| C22×C4×C8 | 13 |