Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C109 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C109×#2679 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2094 | C2 | semidirect |
| 3. C109×#1270 | C2 | semidirect |
| 9. #384×C109 | C22 | semidirect |
| 10. #336×C109 | C22 | semidirect |
| 81. #7822 | C109 | direct (N × H) |
| 87. #2094 | C2×C109 | semidirect |
| 88. #1270 | C2×C109 | semidirect |
| 89. C109 | #7822 | direct (N × H) |
| 95. #384 | C22×C109 | semidirect |
| 96. #336 | C22×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2679 | 2 |
| C109×#2094 | 2 |
| C109×#1270 | 2 |
| #7822 | 109 |