Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
342 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C2×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C13×Q16 | C2 | semidirect |
| 3. C2×C13×#101 | C2 | semidirect |
| 5. C13×#341 | C2 | semidirect |
| 43. #2020 | C13 | direct (N × H) |
| 67. C22×Q16 | C2×C13 | semidirect |
| 68. C2×#101 | C2×C13 | semidirect |
| 70. #341 | C2×C13 | semidirect |
| 122. C13 | #2020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#137 | 2 |
| C22×C13×Q16 | 2 |
| C2×C13×#101 | 2 |
| C13×#408 | 2 |
| C13×#341 | 2 |
| #2020 | 13 |