Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#423 | C2 | semidirect |
| 3. C2×C13×#101 | C2 | semidirect |
| 5. C4×C13×M16 | C2 | semidirect |
| 43. #1967 | C13 | direct (N × H) |
| 66. #423 | C2×C13 | semidirect |
| 67. C2×#101 | C2×C13 | semidirect |
| 69. C4×M16 | C2×C13 | semidirect |
| 123. C13 | #1967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| C13×#423 | 2 |
| C2×C13×#101 | 2 |
| C2×C13×#100 | 2 |
| C4×C13×M16 | 2 |
| #1967 | 13 |