Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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×C103 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C42×C103 |
| Frattini, cosocle | C2×#127 | C22×C103 |
| prime radical | C2×#127×C103 | C22 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ C2×#127×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #518×C103 | C4 | semidirect |
| 8. C2×#100×C103 | C4 | semidirect |
| 11. #353×C103 | C4 | semidirect |
| 14. #331×C103 | C4 | semidirect |
| 132. #7485 | C103 | direct (N × H) |
| 144. C103 | #7485 | direct (N × H) |
| 146. #518 | C4×C103 | semidirect |
| 149. C2×#100 | C4×C103 | semidirect |
| 152. #353 | C4×C103 | semidirect |
| 155. #331 | C4×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#353×C103 | 2 |
| C103×#1887 | 2 |
| C2×#331×C103 | 2 |
| #7485 | 103 |