Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
122 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 74 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×C211 | D4 |
| commutator | C4 | C22×C4×C211 |
| Frattini, cosocle | C2×C4 | C23×C211 |
| socle | C22×C211 | C2×D4 |
| prime radical | C2×D4×C211 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C211 ◁ C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Q8×C211 | C2 | semidirect |
| 4. #106×C211 | C2 | semidirect |
| 5. #103×C211 | C2 | semidirect |
| 7. C4×C8×C211 | C2 | semidirect |
| 11. SD16×C211 | C4 | direct (N × H) |
| 22. Q8×C211 | C2×C4 | semidirect |
| 33. C8×C211 | C2×C4 | semidirect |
| 42. C4×C211 | SD16 | direct (N × H) |
| 49. C211 | C4×SD16 | direct (N × H) |
| 50. C4×SD16 | C211 | direct (N × H) |
| 52. C4×Q8 | C2×C211 | semidirect |
| 54. #106 | C2×C211 | semidirect |
| 55. #103 | C2×C211 | semidirect |
| 57. C4×C8 | C2×C211 | semidirect |
| 61. SD16 | C4×C211 | direct (N × H) |
| 72. Q8 | C2×C4×C211 | semidirect |
| 83. C8 | C2×C4×C211 | semidirect |
| 92. C4 | SD16×C211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C211 | 2 |
| C4×Q8×C211 | 2 |
| C4×D4×C211 | 2 |
| #106×C211 | 2 |
| #103×C211 | 2 |
| #102×C211 | 2 |
| C4×C8×C211 | 2 |
| C4×SD16 | 211 |