Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
170 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 170 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 | C4×C109 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C2×C8×C109 |
| Frattini, cosocle | #408 | C22×C109 |
| socle | C2×C109 | #1326 |
| prime radical | C2×#41×C109 | C2×C4 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C109 ◁ C2×C4×C109 ◁ C22×C4×C109 ◁ #408×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 70. #7377 | C109 | direct (N × H) |
| 78. C109 | #7377 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#1858 | 2 |
| C109×#1321 | 2 |
| C109×#1315 | 2 |
| #7377 | 109 |