Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C2×C13×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×C4⋊Q8 | C2 | semidirect |
| 3. C2×C13×#124 | C2 | semidirect |
| 4. C13×#390 | C2 | semidirect |
| 5. C43×C13 | C2 | semidirect |
| 32. C42×C13 | D4 | semidirect |
| 33. #2858 | C13 | direct (N × H) |
| 49. C2×C4⋊Q8 | C2×C13 | semidirect |
| 51. C2×#124 | C2×C13 | semidirect |
| 52. #390 | C2×C13 | semidirect |
| 53. C43 | C2×C13 | semidirect |
| 62. C4×C13 | #124 | semidirect |
| 94. C42 | D4×C13 | semidirect |
| 95. C13 | #2858 | direct (N × H) |
| 119. C4 | C13×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C4⋊Q8 | 2 |
| C2×C13×#127 | 2 |
| C2×C13×#124 | 2 |
| C13×#390 | 2 |
| C43×C13 | 2 |
| #2858 | 13 |