Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
416 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 162 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 | #381 |
| commutator | C23 | C22×C8×C109 |
| Frattini, cosocle | C22×C8 | C23×C109 |
| socle | C2×C109 | #1817 |
| prime radical | C24×C109 | C2×C8 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C109 ◁ C22×C8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C109×#1378 | C2 | semidirect |
| 103. #12851 | C109 | direct (N × H) |
| 111. #1378 | C2×C109 | semidirect |
| 112. C109 | #12851 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2873 | 2 |
| C2×#349×C109 | 2 |
| C109×#1378 | 2 |
| #12851 | 109 |