Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
584 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2842 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C24×C109 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2070 | C2 | semidirect |
| 48. #32876 | C109 | direct (N × H) |
| 53. #2070 | C2×C109 | semidirect |
| 55. C109 | #32876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2091 | 2 |
| C109×#2070 | 2 |
| C109×#1784 | 2 |
| #32876 | 109 |