Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
682 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 682 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×#2093 | C2 | semidirect |
| 3. C109×#2071 | C2 | semidirect |
| 4. C109×#1270 | C2 | semidirect |
| 5. C109×#1270 | C2 | semidirect |
| 15. #384×C109 | C22 | semidirect |
| 17. #336×C109 | C22 | semidirect |
| 18. #336×C109 | C22 | semidirect |
| 156. #7786 | C109 | direct (N × H) |
| 165. #2093 | C2×C109 | semidirect |
| 166. #2071 | C2×C109 | semidirect |
| 167. #1270 | C2×C109 | semidirect |
| 168. #1270 | C2×C109 | semidirect |
| 169. C109 | #7786 | direct (N × H) |
| 179. #384 | C22×C109 | semidirect |
| 181. #336 | C22×C109 | semidirect |
| 182. #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×#2093 | 2 |
| C109×#2071 | 2 |
| C109×#1270 | 2 |
| #7786 | 109 |