Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #410 |
| commutator | C22×C4 | C22×C4×C109 |
| Frattini, cosocle | C2×#41 | C23×C109 |
| socle | C2×C109 | #1799 |
| prime radical | #532×C109 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C109 ◁ C2×C8×C109 ◁ C2×#131×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C109×#1812 | C2 | semidirect |
| 4. C109×#1391 | C2 | semidirect |
| 5. C2×#131×C109 | C4 | semidirect |
| 11. #423×C109 | C4 | semidirect |
| 13. #408×C109 | C4 | semidirect |
| 15. C2×#97×C109 | C4 | semidirect |
| 130. #12808 | C109 | direct (N × H) |
| 138. #1812 | C2×C109 | semidirect |
| 139. #1391 | C2×C109 | semidirect |
| 140. C109 | #12808 | direct (N × H) |
| 141. C2×#131 | C4×C109 | semidirect |
| 147. #423 | C4×C109 | semidirect |
| 149. #408 | C4×C109 | semidirect |
| 151. C2×#97 | C4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2932 | 2 |
| C109×#2126 | 2 |
| C109×#1812 | 2 |
| C109×#1391 | 2 |
| #12808 | 109 |