Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
1266 conjugacy classes of subgroups; only the 446 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 446 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C109 |
| Frattini, cosocle | C24 | C24×C109 |
| prime radical | C24×C109 | C24 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C23×Q8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4×Q8×C109 | C4 | semidirect |
| 79. #20691 | C109 | direct (N × H) |
| 88. C109 | #20691 | direct (N × H) |
| 91. C2×C4×Q8 | C4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#519×C109 | 2 |
| C109×#2310 | 2 |
| C109×#1820 | 2 |
| C109×#1740 | 2 |
| #20691 | 109 |