Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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 | #99 |
| commutator | C22×C4 | C2×C4×C13 |
| Frattini, cosocle | C2×C22⋊C4 | C22×C13 |
| prime radical | C24×C13 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×Q8×C13 | C4 | semidirect |
| 10. C13×#95 | C4 | semidirect |
| 24. #1351 | C13 | direct (N × H) |
| 68. C22×Q8 | C4×C13 | semidirect |
| 74. #95 | C4×C13 | semidirect |
| 95. C13 | #1351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#393 | 2 |
| C13×#342 | 2 |
| C13×#323 | 2 |
| #1351 | 13 |