Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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×C4⋊C4 | C2×C4×C103 |
| Frattini, cosocle | #382 | C22×C103 |
| prime radical | #537×C103 | C4 |
| LCS | G ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ #382×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#1324 | C2 | semidirect |
| 3. C103×#1295 | C2 | semidirect |
| 97. #7416 | C103 | direct (N × H) |
| 105. #1324 | C2×C103 | semidirect |
| 106. #1295 | C2×C103 | semidirect |
| 107. C103 | #7416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2040 | 2 |
| C103×#1324 | 2 |
| C103×#1295 | 2 |
| #7416 | 103 |