Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
306 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C22×C8 | C23×C109 |
| prime radical | C2×#41×C109 | D4 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ #408×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2236 | C2 | semidirect |
| 3. C109×#2235 | C2 | semidirect |
| 5. C109×#1350 | C2 | semidirect |
| 6. C109×#1350 | C2 | semidirect |
| 145. #12286 | C109 | direct (N × H) |
| 152. #2236 | C2×C109 | semidirect |
| 153. #2235 | C2×C109 | semidirect |
| 155. #1350 | C2×C109 | semidirect |
| 156. #1350 | C2×C109 | semidirect |
| 158. C109 | #12286 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3202 | 2 |
| C109×#2236 | 2 |
| C109×#2235 | 2 |
| C109×#2078 | 2 |
| C109×#1350 | 2 |
| C109×#1315 | 2 |
| #12286 | 109 |