Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
534 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C109 |
| Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C2×#127×C109 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C43×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#1839 | C2 | semidirect |
| 3. C109×#1745 | C2 | semidirect |
| 4. C109×#1270 | C2 | semidirect |
| 144. #7699 | C109 | direct (N × H) |
| 154. #1839 | C2×C109 | semidirect |
| 155. #1745 | C2×C109 | semidirect |
| 156. #1270 | C2×C109 | semidirect |
| 157. C109 | #7699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2858 | 2 |
| C109×#1839 | 2 |
| C109×#1745 | 2 |
| C109×#1270 | 2 |
| #7699 | 109 |