Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
118 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C109 | D4 |
| commutator | C4 | C2×C32×C109 |
| Frattini, cosocle | C4×C16 | C22×C109 |
| socle, prime radical | C22×C109 | C22⋊C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C109 ◁ C4×C16×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. Q8×C109 | C32 | semidirect |
| 52. Q8⋊C32 | C109 | direct (N × H) |
| 59. C109 | Q8⋊C32 | direct (N × H) |
| 90. Q8 | C32×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C16×C109 | 2 |
| C109×C4⋊C32 | 2 |
| C4×C32×C109 | 2 |
| Q8⋊C32 | 109 |