Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
670 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 170 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C2×#127×C109 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#494×C109 | C2 | semidirect |
| 3. C109×#1990 | C2 | semidirect |
| 5. C109×#1273 | C2 | semidirect |
| 119. #10306 | C109 | direct (N × H) |
| 126. C2×#494 | C2×C109 | semidirect |
| 128. #1990 | C2×C109 | semidirect |
| 130. #1273 | C2×C109 | semidirect |
| 131. C109 | #10306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#494×C109 | 2 |
| C2×#486×C109 | 2 |
| C109×#1990 | 2 |
| C109×#1957 | 2 |
| C109×#1273 | 2 |
| #10306 | 109 |