Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C109 |
| prime radical | D4×D8×C109 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C8×D4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2240 | C2 | semidirect |
| 3. C109×#2226 | C2 | semidirect |
| 4. C109×#1675 | C2 | semidirect |
| 5. C109×#1361 | C2 | semidirect |
| 6. C109×#1331 | C2 | semidirect |
| 7. C109×D4⋊C16 | C2 | semidirect |
| 10. #500×C109 | C22 | semidirect |
| 19. C4⋊C16×C109 | C22 | semidirect |
| 22. C4×C16×C109 | C22 | semidirect |
| 23. #335×C109 | C22 | semidirect |
| 143. #12372 | C109 | direct (N × H) |
| 151. #2240 | C2×C109 | semidirect |
| 152. #2226 | C2×C109 | semidirect |
| 153. #1675 | C2×C109 | semidirect |
| 154. #1361 | C2×C109 | semidirect |
| 155. #1331 | C2×C109 | semidirect |
| 156. D4⋊C16 | C2×C109 | semidirect |
| 157. C109 | #12372 | direct (N × H) |
| 160. #500 | C22×C109 | semidirect |
| 169. C4⋊C16 | C22×C109 | semidirect |
| 172. C4×C16 | C22×C109 | semidirect |
| 173. #335 | C22×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C109 | 2 |
| C109×#2240 | 2 |
| C109×#2226 | 2 |
| C109×#1675 | 2 |
| C109×#1361 | 2 |
| C109×#1331 | 2 |
| C109×D4⋊C16 | 2 |
| #12372 | 109 |