Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C24 |
| commutator | C22 | C23×C4×C13 |
| Frattini, cosocle | C2×C4 | C24×C13 |
| socle | C22×C13 | C23×C4 |
| prime radical | C23×C13 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#446 | C2 | semidirect |
| 3. C8×Q8×C13 | C2 | semidirect |
| 34. #2984 | C13 | direct (N × H) |
| 50. #446 | C2×C13 | semidirect |
| 51. C8×Q8 | C2×C13 | semidirect |
| 96. C13 | #2984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C13 | 2 |
| C13×#446 | 2 |
| C8×Q8×C13 | 2 |
| C13×#432 | 2 |
| C13×#431 | 2 |
| #2984 | 13 |