Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| LCS | G ▷ C22×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 |
|---|---|---|
| 28. C2×C8×C13 | Q8 | semidirect |
| 35. C13×C4⋊C4 | Q8 | semidirect |
| 37. #2058 | C13 | direct (N × H) |
| 108. C2×C8 | Q8×C13 | semidirect |
| 115. C4⋊C4 | Q8×C13 | semidirect |
| 117. C13 | #2058 | direct (N × H) |
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×#106 | 2 |
| C13×#389 | 2 |
| C13×#340 | 2 |
| C13×#336 | 2 |
| #2058 | 13 |