Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #393 |
| commutator, Frattini, cosocle | C24 | C23×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C24×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#543 | C2 | semidirect |
| 3. C13×#342 | C2 | semidirect |
| 9. C24×C13 | Q8 | semidirect |
| 16. C22×C4×C13 | Q8 | semidirect |
| 22. #2032 | C13 | direct (N × H) |
| 37. #543 | C2×C13 | semidirect |
| 39. #342 | C2×C13 | semidirect |
| 61. C24 | Q8×C13 | semidirect |
| 68. C22×C4 | Q8×C13 | semidirect |
| 74. C13 | #2032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#543 | 2 |
| C2×C13×#99 | 2 |
| C13×#342 | 2 |
| #2032 | 13 |