Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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×C257 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C257 |
| prime radical | #121×C257 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C257 ◁ C22×C4×C257 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×SD16×C257 | C2 | semidirect |
| 2. C2×M16×C257 | C2 | semidirect |
| 3. C22⋊Q8×C257 | C2 | semidirect |
| 5. #107×C257 | C2 | semidirect |
| 6. #103×C257 | C2 | semidirect |
| 7. #102×C257 | C2 | semidirect |
| 36. C8×C257 | D4 | semidirect |
| 55. C257 | #468 | direct (N × H) |
| 56. #468 | C257 | direct (N × H) |
| 57. C2×SD16 | C2×C257 | semidirect |
| 58. C2×M16 | C2×C257 | semidirect |
| 59. C22⋊Q8 | C2×C257 | semidirect |
| 61. #107 | C2×C257 | semidirect |
| 62. #103 | C2×C257 | semidirect |
| 63. #102 | C2×C257 | semidirect |
| 92. C8 | D4×C257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C257 | 2 |
| C2×M16×C257 | 2 |
| C22⋊Q8×C257 | 2 |
| #121×C257 | 2 |
| #107×C257 | 2 |
| #103×C257 | 2 |
| #102×C257 | 2 |
| #468 | 257 |