Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
262 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 262 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, socle | C2×C109 | #1616 |
| commutator, Frattini, cosocle | C2×M16 | C23×C109 |
| prime radical | C23×C109 | C2×SD16 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C2×C4×C109 ◁ C2×M16×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 87. #12305 | C109 | direct (N × H) |
| 96. C109 | #12305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3261 | 2 |
| C109×#2239 | 2 |
| C109×#2103 | 2 |
| C109×#1342 | 2 |
| C109×#1328 | 2 |
| #12305 | 109 |