Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
424 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 98 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×C109 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C2×#127×C109 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C109×#1574 | C2 | semidirect |
| 4. C109×#1561 | C2 | semidirect |
| 6. C109×#1485 | C2 | semidirect |
| 7. C109×#1299 | C2 | semidirect |
| 159. #10492 | C109 | direct (N × H) |
| 167. #1574 | C2×C109 | semidirect |
| 168. #1561 | C2×C109 | semidirect |
| 170. #1485 | C2×C109 | semidirect |
| 171. #1299 | C2×C109 | semidirect |
| 172. C109 | #10492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3208 | 2 |
| C109×#1965 | 2 |
| C109×#1574 | 2 |
| C109×#1561 | 2 |
| C109×#1545 | 2 |
| C109×#1485 | 2 |
| C109×#1299 | 2 |
| #10492 | 109 |