Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C42 | C23×C13 |
| socle | C22×C13 | C2×C22⋊C4 |
| prime radical | C13×#121 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#432 | C2 | semidirect |
| 3. C2×C4×C8×C13 | C2 | semidirect |
| 4. C13×Q8⋊C8 | C2 | semidirect |
| 5. C13×D4⋊C8 | C2 | semidirect |
| 49. #1494 | C13 | direct (N × H) |
| 71. #432 | C2×C13 | semidirect |
| 72. C2×C4×C8 | C2×C13 | semidirect |
| 73. Q8⋊C8 | C2×C13 | semidirect |
| 74. D4⋊C8 | C2×C13 | semidirect |
| 139. C13 | #1494 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| C13×#432 | 2 |
| C2×C4×C8×C13 | 2 |
| C13×Q8⋊C8 | 2 |
| C13×D4⋊C8 | 2 |
| #1494 | 13 |