Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C24×C13 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C13×#103 | C2 | semidirect |
| 5. C13×#340 | C2 | semidirect |
| 12. C13×C22⋊Q8 | C4 | semidirect |
| 45. #1894 | C13 | direct (N × H) |
| 75. C2×#103 | C2×C13 | semidirect |
| 77. #340 | C2×C13 | semidirect |
| 101. C22⋊Q8 | C4×C13 | semidirect |
| 140. C13 | #1894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×M16 | 2 |
| C2×C13×C22⋊Q8 | 2 |
| C2×C13×#103 | 2 |
| C13×#380 | 2 |
| C13×#340 | 2 |
| #1894 | 13 |